Transcript Section 2.2

Matrix Multiplication
Definition 1: A scalar, in the realm of
matrices, is a real number factor not within
a matrix.
 Definition 2: Scalar
multiplication multiplies a
matrix A by a scalar c. To find the
resulting matrix cA, multiply each
element of A by c.


Prices Use the price list. The cafeteria plans
to raise the cost of each beverage to one
and half times the current cost. How much
will each beverage cost?
Small
Large
Lowfat milk
$0.35
$0.67
Orange juice
$0.65
$0.89
Tomato juice
$0.58
$0.75

Use matrices A and B. Find 5A – 3B.
2
𝐴=
1
3 −7
4 5
3 0
𝐵=
−1 8
6
2

Solve each matrix equation. Check your
answer.
3
4𝑋 + 2
−2
4
10
=
1
4
0
2

Solve each matrix equation. Check your
answer.
7
−3𝑋 +
2
0
−3
−1
10
=
4
−19
0
8
−18 10

Solve the matrix equation.
2𝑋 +
1
3
−2 1
3
1
=
0
11
2
2
19
−
2
−5
12

Definition 3: To perform matrix
multiplication, multiply the elements of
each row of the first matrix by the elements
of each column of the second matrix. Add
the products.

Find each product.
−1
3
0 −3
−4 5
3
0

Find each product.
−3
5
3 −1
0 3
0
−4

Property: Dimensions of a Product Matrix:
◦ If matrix A is an m x n matrix and matrix B is an
n x p matrix, then the product matrix AB is an m
x p matrix.

Determine Whether a Product Matrix Exists.
2 3
𝐺 = −1 8
4 0
8
𝐻=
2
0
−5

Determine Whether a Product Matrix Exists.
4
𝑅=
5
−2
8
𝑆=
−4
2
0 −1
−5 1
0
8

Find the product matrix.
1
9
−3
5
2
4
2
0
1 ∙ −1
5
−8