Row 1 Row 2 Row 3 Row m Column 1Column 2Column 3 Column 4

A matrix of m rows and n columns is called a matrix with dimensions m x n. 2 X 3 3 X 3 2 X 1 1 X 2

3 X 22 X 23 X 3 1 X 22 X 11 X 1

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

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

GUIDED PRACTICE subtraction –4 0 7 –2 – –3 0 5 –14 2. – –6 –2 10 –2 –8 15 ANSWER

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

GUIDED PRACTICE Addition Perform the indicated operation, if possible. + – – –3 1 –5 –2 –8 4 – –14 12 ANSWER

Add and subtract matrices Perform the indicated operation, if possible. 3 0 –5 –1 a. – (–1) –5 + 2 –1 + 0 = = 2 4 –3 –1 –2 5 3 –10 – –2 –1 6 b. – 9 –1 – = 7 – (–2) 4 – 5 0 – 3 –2 – (–10) –1 – (–3) 6 – 1 =

ADDITIVE INVERSE OF A MATRIX:

Find the additive inverse:

Scalar Multiplication: We multiply each # inside our matrix by k.

GUIDED PRACTICE 4 –1 –3 –5 –2 – –3 –2 1 ANSWER

EXAMPLE 2 Multiply a matrix by a scalar Perform the indicated operation, if possible. 4(–2) 4(–8) 4(5) 4(0) –3 8 6 –5 = + a. 4 – –2 –2(4) –2(–1) –2(1) –2(0) –2(2) –2(7) = –8 2 –2 0 –4 –14 = b. 4 –2 –8 5 0 –3 8 6 –5 + –8 – –3 8 6 –5 = +

GUIDED PRACTICE 2 –1 –3 –7 6 1 –2 0 –5 – 4 – –24 – ANSWER Scalar multiplication

Scalar Multiplication:

6x+8=26 6x=18 x=3 10-2y=8 -2y=-2 y=1

GUIDED PRACCE Solve –2 –3x –1 4 y 9 –4 – –18 = + for x and y. x = 5 and y = 6 ANSWER