1. Warm Up
Use scalar multiplication to evaluate the following:

2. Section 4.2: Matrix Multiplication

3. **Multiply rows times columns.
**You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
They must match.
Dimensions:
3 x 2
2 x 3
The dimensions of your answer.

4. Examples: 2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6) 3(3) + 4(5)
3(-9) + 4(7)
3(2) + 4(-6)

5. 2 x 2 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5) 1(4) + 0(-2) 1(-3) +0(5)
*Answer should be a 2 x 2
2 x 2 2 x 2
0(4) + (-1)(-2)
0(-3) + (-1)(5)
1(4) + 0(-2)
1(-3) +0(5)

6. *They don’t match so can’t be multiplied together.*
Dimensions: 2 x x 2
*They don’t match so can’t be multiplied together.*

7. Systems in Matrix Multiplication Form
We can write the following system of equations in Matrix
Multiplication Form:
Take the coefficients of each of the variables and put them in one matrix
The variables go in a second matrix
An equal sign separates the product of the previous matrices and the matrix of the solutions

8. Just to make sure it works…

9. More Practice Multiply the following matrices:
Can you multiply them? Check the dimensions:
What should the new dimensions be?
Set up the multiplication matrix.
R1, C1 =
R2, C1

10. Even More Practice Multiply the following matrices:
Can you multiply them? Check the dimensions:
What should the new dimensions be?
Set up the multiplication matrix.
R1, C R1, C2 =
R2, C R2, C2
R3, C R2, C2