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

2. 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. 3 X 22 X 23 X 3 1 X 22 X 11 X 1

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

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

7. GUIDED PRACTICE subtraction –4 0 7 –2 –3 1 2 2 –3 0 5 –14 2. – –6 –2 10 –2 –8 15 ANSWER

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

10. GUIDED PRACTICE Addition Perform the indicated operation, if possible. + –2 5 11 4 –6 8 1.1. –3 1 –5 –2 –8 4 –5 6 6 2 –14 12 ANSWER

12. Add and subtract matrices Perform the indicated operation, if possible. 3 0 –5 –1 a. –1 4 2 0 + 3 + (–1) 0 + 4 –5 + 2 –1 + 0 = = 2 4 –3 –1 –2 5 3 –10 –3 1 7 4 0 –2 –1 6 b. – 9 –1 –3 8 2 5 = 7 – (–2) 4 – 5 0 – 3 –2 – (–10) –1 – (–3) 6 – 1 =

13. ADDITIVE INVERSE OF A MATRIX:

14. Find the additive inverse:

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

17. GUIDED PRACTICE 4 –1 –3 –5 –2 –2 0 6 3 + 3 –3 –2 1 ANSWER

18. 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 –1 1 0 2 7 –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 –32 20 0 –3 8 6 –5 = +

19. GUIDED PRACTICE 2 –1 –3 –7 6 1 –2 0 –5 – 4 –8 4 12 28 –24 –4 8 0 20 ANSWER Scalar multiplication

21. Scalar Multiplication:

22. 6x+8=26 6x=18 x=3 10-2y=8 -2y=-2 y=1

23. GUIDED PRACCE Solve –2 –3x –1 4 y 9 –4 –5 3 12 10 2 –18 = + for x and y. x = 5 and y = 6 ANSWER