2012 204 MATRICES.doc

MATRICES

NAME : ________________________

Form : _______________matrices_21

1 (a) Find inverse of the matrix .

(b) Hence, using matrices, calculate the value of x and of y that satisfy the following simultaneous linear equations:

(a) [ (b)k = 3, m = 1]

Answer :

2 Given that matrix .

(i) Find the value of k, if G does not have an inverse matrix. (ii) Given that k = 2,

(a) Find inverse matrix of G.

(b) Hence, using matrices, calculate the value of d and of e that satisfy the

following matrix equations:

(i) k =3/4 (ii) (a) (b) d = 6, e = 1Answer :

3 M is a 2 x 2 matrix where .

(a) Find the matrix M.

(b) Write the following simultaneous linear equations as a matrix equation.

3x 2y = 7

5x 4y = 9

Hence, calculate the values of x and y using matrices.

[(a) (b)x = 5, y =4]

Answer :

4 (a) State matrix M if M =

(b) Using matrices, calculate the value of u and w that satisfy the following matrix

equations:

[(a) ,(b) u = 2, w = 4]

Answer :

5 (a) Given that find matrix A.

(b) Hence, using the matrix method, find the value of r and s which satisfy the

simultaneous equations below.

r + 2s = 4

3r + 5s = 9

[(a)A= (b)r = 2, s = 3 ]

Answer :

6 Given matrix P = and matrix PQ =

(a) Find the matrix Q.

(b) Hence, calculate by using the matrix method, the values of m and n that satisfy the following simultaneous linear equations :

4m + 5n = 7

6m + 8n = 10

[(a)Q= (b)m = 3, n = 1]

Answer :7 It is given that matrix P = does not have an inverse matrix.

(a) Find the value of k.

(b) If k = 1, find the inverse matrix of P and hence, using matrices, find the values

of x and y that satisfy the following simultaneous linear equations.

2x + 5y = 13

x 2y = 7

[(a) k = 4/5(b) x = 1, y = 3]

Answer :

8(a) Find matrix M such that M =

(b) Using matrices, calculate the values of x and y that satisfy the following matrix equation.

[(a)M= x = 1, y = 2]

Answer :NAME : ________________________

Form : _______________Matrices_229(a) Find the inverse of matrix

(b) Hence, using matrices, calculate the values of d and e that satisfy the

following simultaneous equations :

2d e = 7

5d e = 16

[(a) (b) d = 3, e = 1]

Answer :

10 Given matrix M = , find

(a) the inverse matrix of M(b) hence, using matrices, the values of u and v that satisfy the following simultaneous equations :

u 2v = 8

2u + 5v = 7

[(a) (b)u = 6, v = 1]

Answer : (TRIAL SBP 2006)

11.(a) Given that the inverse of is . Find the values of m and n.

(b)Hence, using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations:

( x + 4y = 9

x + y = 6

[ a) m = 3, n = 1 b) x = 5, y = 7/2 ]

(SBP 2005)12.(a)M is a 2 ( 2 matrix where M= . Find the matrix M.


[ a) b) x = 3, y = 4 ]

(TRIAL SBP 2004)

13.(a)Given that , find the values of k and p.


[ a) p = 2 , k = 1/3 b) x = 5/3 y = 2/3 ]

(TRIAL JOHOR 2006)

14.(a)Given that matrix M = , find the matrix P if MP = .

(b)Hence, using matrices, calculate the values of a and b which satisfy the following simultaneous linear equations:

2a + b =

a b =1

[ a) b) a = 4, b = 5 ]

(TRIAL SELANGOR 2006)

15.(a)Q is a 2 ( 2 matrix where Q =

Find the matrix Q.

(b)Using matrices, calculate the values of h and k which satisfy the following simultaneous linear equations:

[ (a) (b) h = 4, k = 6 ]

(TRIAL PAHANG 2003)16.Given that matrix P = and matrix Q = .

(a)Find the value of w if PQ = .

(b)Hence, using matrices, calculate the values of x and y which satisfy the following equation.

EMBED Equation.3 =

[ (a) w = 2 (b) x = 2, y = 2 ]

NAME : ________________________

Form : _____________Matrices_23(TRIAL KELANTAN 2003)

17.(a) Given that

EMBED Equation.3

EMBED Equation.3 =, find the value of b.

(b)Hence, using matrices, calculate the values of x and y which satisfy the following matrix equation.

EMBED Equation.3 =

[(a) b = 2 (b) x = 3, y= 2]

(TRIAL KEDAH 2005)

18.(a)Given that matrix E = and the inverse matrix of E =

EMBED Equation.3 .

Find the values of m and r.

(b)Hence, using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations.

2x 3y = 14

x + 3y = 13

[ (a) r = 2, m = 3 (b) x = 1, y = 4]

(TRIAL MRSM 2005)

19.(a)Given that matrix P is 2 x 2 matrix where P . Find the matrix P.

(b)Hence, using matrices, calculate the values of m and n which satisfy the following simultaneous linear equations.

2m 3n = 8

m + n = 6

[(a) (b) x = 76, y = 48 ]

(TRIAL JOHOR 2005)

20.(a)Given that matrix A = , find the inverse matrix of A.

(b)Hence, using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations.

6m 4n = 8

7m + 5n = 9

[ a) b) m = 2, n = 1]

21(a)Find the inverse matrix of

(b)Using matrices, calculate the value of k and of m that satisfy the following simultaneous linear equations:

2k + 4m = 10

k + 3m = 8

[(a) b) k = 1, m = 3 ]

22(a)Given that matrix . Find the matrix Q if .

(b)Hence, by using matrices, calculate the value of u and of w that satisfy the following matrix equation:

8u + 4w = 4

3u 2w = 0 [(a)

(b)u = 2, w = 3]

23Given that is the inverse matrix of .

(i)Find the value of r and of k.

(ii) Hence, by using matrices, find the value of x and of y which satisfy the following equation:

x y = 11

2x + 3y = 2 [(i)r = 2, k =5(ii)x = 7, y = 4 ]

24Given matrix , matrix and matrix .

(a). Find the value of k and of m.

(b). Hence, by using matrices, find the value of x and of y which satisfy the following matrix equation:

6x 5y = 4

3x 2y = 7 [(a). k = 2, m = 3.(b). x = 9, y = 10]

NAME : ________________________

Form : ______________Matrices_2425(a)Given the matrix equation .

Find the value of p and of k.

(b)Hence, by using matrices, find the value of x and of y which satisfy the following equation:

x 3y = 8

4x + 5y = 15 [(a)p = 3 , k = 1/17.(b)x = 5, y = 1]

26(a)Given , find the value of m and of n.

(b)Using matrices, calculate the value of u and of w that satisfy the following matrix equation:

8u 9w = 5

2u 3w = 1

[(a)m = 8 , n = 6. (b)u = 4, w = 3.]

27M is a matrix such that

(a). Find matrix M.

(b). Write the following simultaneous linear equation as matrix equation:

3x 2y = 12

5x 4y = 22Hence, using matrices, calculate the value of x and of y.

[(a). (b). x = 2, y = 3]

28(a)Find the matrix M if .

(b)By using matrices, calculate the value of u and of w that satisfy the following matrix equation:

5u + w = 6

3u + 2w = 2 [(a).(b)u = 2, w = 4. ]

29Given that matrices , and ,

(i)Find the value of m if KL =I(ii) By using matrices, find the value of t and of u which satisfy the following equation:

t 2u = 6

4t 6u = 22

[(i)m = (ii)t = 4, u = 1.]

30It is given that matrix and matrix

(a)Find matrix Q.

(b)Hence, by using matrices, calculate the value of x and of y that satisfy both of the following equations:

3x + y = 5

7x + 4y = 10 [(a). (b)x = 2, y = 1]

31.Find the inverse matrix of G = .

Using matrices, calculate the values of x and y which satisfy both of the following equations.

3x 4y = 7

x + 2y = 4

[ (a) (b) x = 3 , y = ]

32 a) Find the inverse matrix of .

b) Using matrices, calculate the values of m and n that satisfy the following simultaneous linear equations.

3m + 2n = 4

4m + 5n = 17

. [ a.

EMBED Equation.3 b. m = 2 , n = 5]

NAME : ________________________

Form : _______________Matrices_2533. F is a 2 matrix where F =.

Find the matrix F.

Write the following simultaneous linear equations as a matrix equation.

2p q = 10

5p 4q = 34

Hence, calculate the values of p and q using matrices.

[a.

EMBED Equation.3 b. p =2, q = 6]

34. Given that H = .

Calculate the value of k for which matrix H has no inverse matrix.

Given that k = 2,find the inverse matrix of H.

Hence, calculate the values of d and e which satisfy the following matrix equation.

EMBED Equation.3 =

. [ a. k = 6/5 ;

EMBED Equation.3 b. d = 3, e = 1]

35It is given that the matrix equation

EMBED Equation.3

EMBED Equation.3 = .

a) Find the value of p and of q.

b) Write the following simultaneous linear equations as a matrix equation.

6x + y = 9

3x2y =13

Hence, use the matrix method to calculate the value of x and of y.

. [ a. p = 3, q = 15 b. x = 1/3 , y = 7]

36. a) It is given that matrix A = and its inverse matrix =

EMBED Equation.3 . Find the value of m and of n.

b) Use the matrix method to calculate the values of x and of y which satisfy the following matrix equation.

[ a. m = 2, n = 4 b. x = 25/12, y = 41/6 ] 37. a. Given matrix P = and matrix Q such that PQ = .Find matrix Q.

b. It is given that


Find the values of e,f,g and h.

[ a.Q = b. e = , f = 3, g = , h = 2]

38. a) Find the inverse matrix of .

b) Using matrices, calculate the values of m and n that satisfy the following simultaneous linear equations.

3m + 2n = 4

4m + 5n = 17

[ a.

EMBED Equation.3 b. m = 2 , n = 5]39. F is a 2 matrix where F =.

a) Find the matrix F.


2p q = 10

5p 4q = 34

Hence, calculate the values of p and q using matrices.

[a.

EMBED Equation.3 b. p =2, q = 6]

40. Given that H = .

a)Calculate the value of k for which matrix H has no inverse matrix.

b)Given that k = 2,find the inverse matrix of H.

c)Hence, calculate the values of d and e which satisfy the following matrix equation.

EMBED Equation.3 =

[a. k=6/5, b.

EMBED Equation.3 (c) d = 3 , e = 1 ]NAME : ________________________

Form : _______________Matrices_2641. It is given that the matrix equation

EMBED Equation.3


a) Find the value of p and of q.


6x + y = 9

3x2y = 13

Hence, use the matrix method to calculate the value of x and of y.

[ a. p = 3, q = 15 b. x = , y = 7]

42. a) It is given that matrix A = and its inverse matrix =

EMBED Equation.3 . Find the value of m and of n.

b) Use the matrix method to calculate the values of x and of y which satisfy the following matrix equation.

A =

[a. m = 2, n = 4 , b. x = 5 , y = 2]

43 M is a 2 x 2 matrix where M () = ()

a)Find the matrix M

b)Write the following simultaneous linear equation as a matrix equation.

3 x 2 y = 7

5 x 4 y = 9

Hence , calculate the values of x and y using matrices.

[ a. b. x = 5 , y = 4]44 a) The inverse matrix of is m

Find the value of m and of p.

[ m = , p = 4 ]

b) Using matrices, calculate the value of x and of y that satisfy the following simultaneous linear equation:

3x 4y = 1

5x 6y = 2

[a. m = , p = 4 b. x = 7 , y = 11/2]

45 It is given that matrix P = and matrix Q = k such that PQ = .

a)Find the value of k and of h.

b)Using matrices , find the value of x and of y that satisfy the following simultaneous linear equation:

2x 5y = 17

x + 3y = 8

[a. k = 1/11 , h = 5 b. x = 1 , y = 3]

46 a)It is given that is the inverse matrix of . Find the value of n.

b)Write the following simultaneous linear equations are matrix equation:

3u 4v = 5

u + 2v = 2

hence , using matrices , calculate the value of u and of v.

[a. n = 3/2 (b) u = 1 , v = ]

47. M is a 2 2 matrix where M = .


(b)Write the following simultaneous linear equation as a matrix equation.

3x 2y = 7

5x 4y = 9

Hence, calculate the values of x and y using matrices. [SPM Nov 2003]

(a) (b) x = 5 , y = 4 ]

48. (a) Find the inverse matrix of

(b)Using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations.

2x + 3y = 1

5x + 6y = 2

[SPM June 2004]

(a) (b) x = 4, y = 3NAME : ________________________

Form : _____________Matrices_2749. (a) The inverse matrix of is .

Find the values of m and p.(b)Using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations.

3x 4y = 1

5x 6y = 2

[SPM Nov. 2004]

(a) m = p= 4 (b) x = 7 y = 11/2

50. P is a 2 2 matrix where

P = .

(a) Find the matrix P.


x 2y = 8

3x + 4y = 6


[SPM Jun 2005]

(a) (b) x = 2, y = 351. It is given that matrix P = , matrix Q = such that PQ = .

(a)Find the value of k and of h.


2x 5y = 17

x + 3y = 8

[SPM Nov. 2005]

(a) k = 1/11 h = 5 (b) x = 1 y = 3 ]

52. It is given that matrix .

(a)Find the inverse matrix of M.

(b)Write the following simultaneous linear equations as matrix equation:

Hence, using matrices, calculate the value of x and of y.

[SPM June 2006]

(a) (b)x = 5, y =

53. (a) It is given that is the inverse matrix of . Find the value of n.

(b) Write the following simultaneous linear equation as matrix equation:

3u 4v = 5

u + 2v = 2

Hence, using matrices, calculate the value of u and of v.

[SPM Nov. 2006]

[ (a) n = 3/2 (b) u = 1 v = ]

54. (a) Find the inverse matrix of .


x 2y = 4

3x + 4y = 2


[SPM June 2007](a) (b) x = 2, y = 155. (a) Given that

EMBED Equation.3

EMBED Equation.3 =, find the value of m and of n.

(b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation:

=

[SPM Nov 2007]

[( a) m= 2 n = 3 (b) x = y = 3/2 ]

56. (a) Given that

EMBED Equation.3

EMBED Equation.3 =.

Find the value of p and of q.

(b) Write the following simultaneous linear equations as matrix equation:

Hence, using matrix method, calculate the value of x and of y. [(a) p = 10 , q=3 (b) x = 3, y = ]

Name : __________________________________

Form : _________________Matrices_2857.The inverse matrix of is .

(a) Find the value of m and of k.


Hence, using matrix method, calculate the value of x and of y.

[

[ (a) x = 11, y =7 (b) k = 2 m = 4 ]

58. It is given that matrix P =

(a) Find the inverse matrix of P

(b) Write the following simultaneous linear equations as matrix equation

Hence , by using matrix method ,calculate the value of x and the value of y

(a) (b) x = 1. y = 2

59. M is a 2 2 matrix where M = .



3x 2y = 7

5x 4y = 9

Hence, calculate the values of x and y using matrices. [SPM Nov 2003]

(a) (b) x = 5 ;y = 4

60. (a) Find the inverse matrix of


2x + 3y = 1

5x + 6y = 2

[SPM June 2004] (a) (b) x = 4, y = 3 61. (a) The inverse matrix of is .

Find the values of m and p.(b)Using matrices, calculate the values of x and y which satisfy the following simultaneous linear equations.

3x 4y = 1

5x 6y = 2

[SPM Nov. 2004]

(a) m = , p = 4 (b) x = 7 , y =

62. P is a 2 2 matrix where

P = .

(a) Find the matrix P.


x 2y = 8

3x + 4y = 6


[SPM Jun 2005] (a) (b) x = 2, y = 363. It is given that matrix P = , matrix Q = such that PQ = .

(a)Find the value of k and of h.


2x 5y = 17

x + 3y = 8

[SPM Nov. 2005]

(a) k = 1/11, h = 5 (b)x = 1, y = 3

64. It is given that matrix .

(a)Find the inverse matrix of M.

(b)Write the following simultaneous linear equations as matrix equation:

Hence, using matrices, calculate the value of x and of y.[SPM June 2006] (a) (b) x = 5, y =

(

Name : __________________________________

Form : __________________Matirces_2965. (a) It is given that is the inverse matrix of . Find the value of n.


3u 4v = 5

u + 2v = 2

Hence, using matrices, calculate the value of u and of v.

[SPM Nov. 2006]

(a) n = 3/2 (b) u = 1, v =1/2

66. (a) Find the inverse matrix of .


x 2y = 4

3x + 4y = 2


[SPM June 2007]

(a) (b) x = 2 y = 1 67. (a) Given that

EMBED Equation.3

EMBED Equation.3 =, find the value of m and of n.

(b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation:

=

[SPM Nov 2007](a) m = 2 , n = 3 (b) x =1/2 , y = 3/2

68. (a) Given that

EMBED Equation.3

EMBED Equation.3 =.

Find the value of p and of q.



[ SPM June 2008 ]

(a) q = 3, p = 10 (b) x = 3, y =

69.The inverse matrix of is .

(a) Find the value of m and of k.


Hence, using matrix method, calculate the value of x and of y. [SPM Nov 2008]

(a) k = 2 , m = 4 (b) x = 11, y =7

70. It is given that matrix P =

(a) Find the inverse matrix of P

(b) Write the following simultaneous linear equations as matrix equation

Hence , by using matrix method ,calculate the value of x and the value of y

SPM June 2009

(a) (b) x = 1. y = 2

71. It is given that matrix is

Diberi bahawa matriks

(a) Find the inverse matrix of A.

Cari matriks songsang bagi A.(b) Write the following simultaneous linear equations as matrix equation:

Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks:


Seterusnya, menggunakan kaedah matriks, hitung nilai x dan nilai y.

[ SPM NOV 2009 ]

(a) (b) x = 2 y = 1

72, The inverse matrix of is [7M]

Matriks sonsang bagi ialah a)Find the value of m and k

Cari nilai m dan k

b)Write the following simultaneous linear equations as matrix equation.

Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.

Hence , using the matrix method , calculate the value of x and y.

Seterusnya , dengan menggunakan kaedah matriks, hitung nilai xand nilai y.

SPM NOV 2010

(a) m = 4 , k = 1/22 (b) x = 3/2 y = 1]Name : _______________________________________________

Form : _________________________Matrices_21073) a) Given that E is the matrix , find the matrix F such that EF =

b) Using matrices, calculate the values of m and n which satisfy the following matrix

equation.

EMBED Equation.3 =

(a) (b) m = 26 , n = 34

74) When solving the matrix equation

EMBED Equation.3 =, it is found that

=

EMBED Equation.3

EMBED Equation.3 a) Find the values of k, p, q, r and s.

b) Hence, find the values of x and y

(a) k = 9 , p = 3, q = 0 , r = 2 , s = 3 (b) x = 4 y = 1

75) a) Find the inverse matrix of G =

b) Using matrices, calculate the values of x and y which satisfy both of the following

equations.

3x 4y = 7

x + 2y = 4

(a) (b) x 3 , y =

76) a) Given that the inverse matrix of is , state the value of h and k.

b) Using matrices, calculate the values of x and y which satisfy both of the following

equations.

4x + 5y = 1

3x + 2y = 8

(a) h = 2/7 , k = 3/7 (b) x = 6 y = 5

77) a) Given that F is the matrix and the inverse matrix of F is

EMBED Equation.3 find the value of m and n.

b) Hence, calculate the values of x and y which satisfy the following matrix equation.

F=

(a) ) m = 5 , n = 4 (b) x = 1 , y = 1

78) a) Find the inverse matrix of

b) Hence, calculate the values of h and k which satisfy the following matrix equation.

EMBED Equation.3 =

(a) (b) h = 1/2 , k = 3/2

79) a) Given that M is the matrix and the inverse matrix of M is

EMBED Equation.3 ,

Find the values of k, m and n

b) hence, calculate the values of x and y which satisfy the following matrix equation.

M=

(a) k = 4 , m = 1, n = 3 (b ) x = 2 y = 1

80) Given that E = and F = ,

a) Find the value of k where EF =

b) State the inverse matrix of E

c) Hence, using matrices, find the value of x and y which satisfy the following matrix

equations.

EMBED Equation.3 =

(a) k = 6 (b) (c) x=2 ,y = 1

Name : _________________________________

Form : _________________Matices 2_1181) a) The inverse matrix of is m , find the value of m and p.

b) Using matrices, calculate the value of x and y which satisfy the following simultaneous linear equations.

2x + y = 4

3x 4y = 17

(a) m = 1/11 , p = 3 (b) x = 3 y = 2

82) a) It is given that matrix M = , find the inverse matrix of M

b) Using matrices, find the values of x and y which satisfy the following equations.

3x + 4y = 11

x + 2y = 7

(a) (b) x= 3 , y = 5

83) Given that the inverse matrix of is .

(a)Find the value of m and of n.

(b)Hence, using matrices, calculate the values of d and e in the following

simultaneous linear equations :

2d + e = 7 2d 3e = 1

(a) m = 4 , n = 2 (b) d = e = 5 , y = 3 ]

84) (a)Given , find the value of m and n.

(b) Using matrices, calculate the value of x and y that satisfy the following matrix

equation :

(a) m = 10 , n = 4 (b) x = 5 y = 1

85) (a) Given that matrix and matrix .

Diberi matriks dan matriks .

Find the value of s such that .

Cari nilai s dengan keadaan .

(b) Write the following simultaneous linear equations as a matrix equation.

Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.


Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan y . (a) s = 3/2 (b) x = 3 , y =

86. (a)The inverse matriks of is

Find the value of p and of r

Matriks songsang bagi ialah

Carikan nilai p dan nilai r

(b) Using matrices, calculate the value of x and of y that satisfy the following simultaneous liner equation:

Dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan pesamaan linear serentak berikut:

2x + 5y = 12

x + 4y = 3

[ (a) p = 3 r = 4 (b) x = 11 , y = 2 ]

87. (a) Given , find the value of k and of p.

Diberi ,

tentukan nilai k dan nilai p.

(b)Hence, by using matrices, calculate the value of x and of y that satisfy the following simultaneous linear equations.

Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak berikut

[ (a) k = p = 4 (b) x = 2 y = 5 ]

88. (a) It given that matrix P = , find the value of n if matrix P not have inverse matrix.

If n = 5,find the inverse matrix of P.

Diberi matriks P = , cari nilai n jika matriks P tidak mempunyai songsang .

Jika n = 5, cari matriks songsang bagi P.

(b)Hence, by using matrices, calculate the value of x and of y that satisfy the equations.

Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai v dan nilai w yang memuaskan pesamaan itu.

[ (a) n = 3/2 inverse P = x = 1 , y = 2 ]

Name : _______________________________

Form : ___________________Matirces 2_1289. M is a matrix 2 ( 2 such that M

M ialah satu matriks 2 ( 2 dengan keadaan M


Carikan matriks M.(b) Write the following simultaneous linear equations as a matrix equation .

Tuliskan persamaan serentak berikut dalam bentuk persamaan matriks .

4x + 3y = 23

7x 5y = 11

Hence, by using matrices, calculate the value of x and of y that satisfy the equations.

Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan pesamaan itu. [ (a) Inverse M = (b) x = 2 , y = 5 ] 90. Given that matrix A = and matrix B = such that AB = . Diberi bahawa matriks A = dan matriks B = dengan keadaan AB = .(a)Find the value of k and value of h.

Carikan nilai k dan nilai h.

(b) Using matrices, find the value of x and of and of y that satisfy the following

simultaneous linear equations.

Dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak berikut :

3x + 2y = 6

8x + 4y = 4

[ (a) k = h = 3 (b) x = 4 , y = 9 ]91. Given that matrices P = and Q = ,

Diberi bahawa matriks P = dan Q = ,

(a)Find

Carikan

(i) the value of k, if matrix P has no inverse

nilai k, jika matriks P tidak mempunyai songsang,

(ii)the inverse of matrix Q.

matriks songsang bagi Q.

(b) Using matrices, calculate the value of x and the value of y that satisfy the following simultaneous equations : Dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak berikut :

2x + y = 4

3x 2y = 13

[ (a)(i) k = (ii) h = 3 (b) x = 3 , y = 2 ]92. Given M is a 2 2 matrix such that

Diberi M ialah satu matrik 2 2 dengan keadaan

M

EMBED Equation.3 =




3x + 6y = 12 x + 4y = 10 Hence, by using matrices, calculate the value of x and of y that satisfy the equations.

Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan pesamaan itu. [ (a) M = (b) x = 2 y = 3 ]93. (a) Given that x

EMBED Equation.3 =,

find the value of x and of y.

Diberi x

EMBED Equation.3 =, carikan nilai x dan nilai y.

(b) Write the following simultaneous linear equations as a matrix equation .


6v 4w = 4

7v 5w = 7

Hence or otherwise find the values of v and w .

[ (a) x = y = 4 (b)

v = 4 , w = 7 ]

94. Given M is a 2 2 matrix such that

Diberi M ialah satu matrik 2 2 dengan keadaan

M

EMBED Equation.3 =




3x + 6y = 12 x + 4y = 10 Hence, by using matrices, calculate the value of x and of y that satisfy the equations.

Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan pesamaan itu.

[ (a) (b) x = 2 , y = 3]

95. Given A = and the inverse matrix of A is

EMBED Equation.3 Diberi A = dan matriks songsang bagi A ialah

EMBED Equation.3 (a)Find the value of m and n.(a)Carikan nilai bagi m dan n.(b)Write the following simultaneous linear equations as matrix equation:

(b) Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks:5x + 8y = 4

x + 2y = 2

Hence, using matrices, calculate the value of x and of y.Seterusnya, dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y [ (a) m = 8 n = 2 (b)

x = 12 , y = 7 ]

96. Given that matrices P = and Q = ,

Diberi bahawa matriks P = dan Q = , (a)Find

Carikan

(j) the value of k, if matrix P has no inverse

nilai k, jika matriks P tidak mempunyai songsang,

(ii)the inverse of matrix Q.

matriks songsang bagi Q.

(a) Using matrices, calculate the value of x and the value of y that satisfy the following simultaneous equations : Dengan menggunakan kaedah matriks, hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak berikut :

2x + y = 4

3x 2y = 13

[ (a) (i) k = 3 (ii) (ii) x = 3 , y = 2 ] EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

PAGE 48

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2012 204 MATRICES.doc