HL MATH SAMPLE PROBLEM 050 BROSE

GIVEN: 2 3 8

5 2 1

x y

x y

Solve for x and y using :

A) Inverse Matrix Method

B) Gaussian Elimination

Inverse Matrix Method

1

2 3 8

5 2 1

2 3 8

5 2 1

2 3 8

5 2 1

2 3 81

19 5 2 1

191

19 38

1 1

2 2

x y

x y

x

y

x

y

x

y

x

y

x x

y y

Gaussian Elimination

2 3 8

5 2 1

2 3 8 2 2 1

5 2 1

1 8 15 2 5 1

5 2 1

1 8 15 2

0 38 76 38

1 8 15 1 8 2

0 1 2

1 0 1 1 0 | 1

0 1 2 0 1 | 2

1

2

x y

x y

R R

R R

R

R R

x

y

HL MATH SAMPLE PROBLEM 050 BROSE

Inverse Matrix Method

1

3 2 2

5 4 2 7

2 5 15

3 2 1 2

5 4 2 7

2 1 5 15

3 2 1 2

5 4 2 7

2 1 5 15

Use Calc or see notes

18 90

99 99

x y z

x y z

x y z

x

y

z

x

y

z

x

y

z

229 13 11

7 99 99 99

1513 1 22

99 99 99

1

2

3

x

y

z

Gaussian Elimination

3 2 2

5 4 2 7

2 5 15

3 2 1 2

5 4 2 7 1 3

2 1 5 15

1 1 4 13

5 4 2 7 2 5 1

2 1 5 15

1 1 4 13

0 9 18 72 3 2 1

2 1 5 15

1 1 4 13

0 9 18 72 2 9

0 1 13 41

1 1 4 1

0 1 2

0 1 13

x y z

x y z

x y z

R R

R R

R R

R

3

8 3 2

41

1 1 4 13

0 1 2 8 3 3

0 0 1 3

1 1 4 13

0 1 2 8 1 2

0 0 1 3

1 0 2 5

0 1 2 8 1 2 3

0 0 1 3

1 0 0 1

0 1 2 8 1 2 3

0 0 1 3

1 0 0 | 1

0 1 0 | 2 2 2 3

0 0 1 | 3

1,

R R

R

R R

R R

R R

R R

x

2, 3 y z