Transcript Section 2.2

Matrix Multiplication

Definition 1: 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

Find the difference 5A-3B for 𝐴 =
2 3 −7
3 0 6
𝑎𝑛𝑑 𝐵 =
.
1 4 5
−1 8 2

Solve each matrix equation. Check your
answer.
3 4
10 0
4𝑋 + 2
=
−2 1
4 2
7 0 −1
10
0
8
−3𝑋 +
=
2 −3 4
−19 −18 10

Definition 2: 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 0 −3 3
3 4 5 0
−3 3 −1 0
5 0 3 −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
8 0
𝐺 = −1 8 𝑎𝑛𝑑 𝐻 =
2 −5
4 0
𝐷𝑜𝑒𝑠 𝐺𝐻 𝑒𝑥𝑖𝑠𝑡 𝑎𝑛𝑑 𝑑𝑜𝑒𝑠 𝐻𝐺 𝑒𝑥𝑖𝑠𝑡?
4 −2
8 0 −1
𝑅=
𝑎𝑛𝑑 𝑆 =
5 −4
2 −5 1
𝐷𝑜𝑒𝑠 𝑅𝑆 𝑒𝑥𝑖𝑠𝑡 𝑎𝑛𝑑 𝑑𝑜𝑒𝑠 𝑆𝑅 𝑒𝑥𝑖𝑠𝑡?