1. Multiplying Matrices

2. Introduction to Matrices
Section 7.5
Introduction to Matrices
Matrix
____________ arrangement of terms.
Each term is called an ___________.
Arranged in _____ and __________.
A matrix with an a x b dimension has ___ ________ and ___ ________.
Rectangular
element
rows
columns a
rows b
columns

3. Row 1 Row 2 Row 3 Column 1 Column 2 2 x 2 Matrix 2 x 3 Matrix
Row 2
Row 3
Column 1
Column 2

4. Adding or Subtracting Matrices
Dimensions must be the _______.
Add/Subtract elements that are in the ______ ___________.
Scalar Multiplication with Matrices
Multiply number to all __________.
same
same
position
elements

5. Examples
1. A + B
3 0 −1 5
5 1 −3 4
3 −1
A =
B =
C =
= −1+(−3) 5+4
= −4 9

6. 3 0 −1 5 5 1 −3 4 3 −1 = 3−5 0−1 −1−(−3) 5−4 = −2 −1 2 1 2. A – B A =
C =
= 3−5 0−1 −1−(−3) 5−4
= −2 −1 2 1

7. 3 0 −1 5 5 1 −3 4 3 −1 = 5−3 1−0 −3−(−1) 4−5 = 2 1 −2 −1 3. B – A A =
C =
= 5−3 1−0 −3−(−1) 4−5
= −2 −1

8. Scalar Multiplication - each element in a matrix is multiplied by a constant.

9. 3 0 −1 5
5 1 −3 4
3 −1
4. 5C 5. –3B
A =
B =
C =
= 5 3 −1
= 15 −5
= – −3 4
= −15 −3 9 −12

10. **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.

11. 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)

12. *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.*

13. 2 x 2 2 x 2 *Answer will be a 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5)
1(4) + 0(-2)
1(-3) +0(5)