PSAT/SAT Special Symbol Practice1.

2. x = 140

3. 25

4. r = –1

5. E) 11 – a

6. D) 20

7. B) 1

8. a = 36

9. 27

10. xy = 125

1 215 5.25

4 4

Students are allowed to use their own calculators on the PSAT - scientific or graphing calculators are recommended. Students are not allowed to use the following, however:1. pocket organizers2. laptops and handheld devices3. cell phone calculators4. calculators with a QWERTY keypad5. calculators that require an electrical outlet

Also, students can't share calculators. Math questions on the PSAT can be solved WITHOUT a calculator but students are allowed to use one if they bring their own. We will not be providing students with calculators for the PSAT.

11 12 13 14

21 22 23 24

31 32 33 34

mn mn mn mn

a a a a

a a a a

a a a a

a a a a

Row 1

Row 2

Row 3

Row m

Column 1 Column 2 Column 3 Column 4

A matrix of m rows and n columns is called a matrix with dimensions m x n.

That’s Row x Column

And a…

2 3 41.) 1

12

3 8 9

2.) 2 5

6 7 8

103.)

7

4.) 3 4

2 X 3 3 X 3

2 X 11 X 2

11

21

31

7

4

1

a

A a

a

21... 4So a

b34 = –7

b42 = – 5

b54 = 3

e32 = –2

g21 = –3

d21 = Does not exist

7 in X x21

0 in U u11

-5 in P p12

Addition and Subtraction of

Matrices

To add matrices, we add the corresponding elements. They must have the same dimensions.

5 0 6 3

4 1 2 3A B

A + B5 6 0 3

4 2 1 3

1 3

6 4

N + O = No can do! Must have the same dimensions!

2 1 3 0 0 02.)

1 0 1 0 0 0

2 1 3

1 0 1

When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.

To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.

1 2 1 1

3.) 2 0 1 3

3 1 2 3

0 3

3 3

5 4

1 3 2 2 1 51.)

4 0 5 6 4 3

1 4 7

2 4 8

2.) T + U – S =13 11

8 10

ADDITIVE INVERSE OF A MATRIX:

1 0 2

3 1 5A

1 0 2

3 1 5A

Scalar Multiplication:

1 2 3

1 2 3

4 5 6

k

We multiply each # inside our matrix by k.

1 2 3

1 2 3

4 5 6

k k k

k k k

k k k

3 01.) 3

4 5

9 0

12 15

2

1 2

2.) 5 4 1

0 5

x

y

x

2

5 10 5

20 5 5

0 25 5

x

y

x

6 5 6 5

8 4 14 4

0 2 1 0 13

x x

y y

x + 8 = 14 – x

2x = 6 x = 3

2y – 1 = – 13 – y

3y = – 12 y = – 4

812

026

2

14

58

132

y

x

812

026

528

11432

y

x

812

026

56

0432

y

x

812

026

21012

086

y

xScalar Multiplication:

6x+8=26

6x=18

x=3

10-2y=8

-2y=-2

y=1

Homework•Page 41 #1 – 15 FC •Page 42 #1 – 14 FC

FC means (1st column)