1. Section 3.1 – Operations with Matrices
No Calculator

2. Matrix – an array (set) of numbers arranged in rows and columns
Dimension of a Matrix – number of rows x number of columns
2 x 2
3 x 2
4 x 1
2 x 3
1 x 1
1 x 3

3. Addition of Matrices
Dimensions MUST be the same for sum to exist
Sum - DNE
Sum - DNE

4. Subtraction of Matrices
Dimensions MUST be the same for sum to exist
Sum - DNE
Sum - DNE

5. Scalar – a number
SCALAR Multiplication
(always works)

6. MATRIX MULTIPLICATION
Order makes a difference…AB is different from BA
Number of columns in first matrix must equal number of
rows in second matrix. (middle numbers match)
Answer will be number of rows in first matrix by number of
columns in second matrix. (outside numbers)
Are the following matrix multiplications possible?
2 x 1
1 x 2
1 x 2
2 x 1

7. Are the following matrix multiplications possible?
3 x x 2 NO
2 x x 2
YES
3 x x 3
YES
3 x x 3
YES
2 x x 2
YES
3 x x 2 NO

8. What is the dimension of the answer going to be?
3 x x 2 NO
2 x x 2
YES
2 x 2
3 x x 3
YES
3 x x 3
YES
3 x 3
3 x 3
2 x x 2
YES
3 x x 2 NO
2 x 2

11. MATRIX MULTIPLICATION STEPS
1. Is the multiplication possible? (middle numbers match)
2. If yes, what is the dimension of the answer? (outside numbers)
3. Create “blank” matrix.
4. “Multiply/Add” corresponding rows and columns