 # Matrix Operations

Warm-up

1. Identify the rows and columns in the array of numbers. Rows : A, B, C
Columns: D, E, F, G

2. In the above array of numbers, what number is in the second row, third column?

0

3. Write 4% as a decimal .

.04

4. What is 100 increased by 4% of 100?

104

5. Find this product : 1.04 ·100.

104

6. Suppose you want to increase a number by 6%. How can you do this using one
operation
?

Multiply by 1.06

Section 3-5 Matrix Operations

Matrix: An arrangement of numbers in rows and columns. Plural is matrices.

Elements of a matrix: The numbers in the matrix.
Example: The element is Row 2 Column 3 is 0.

Dimensions of a matrix: Number of rows by the number of columns.
Example: 3 x 4 are the dimensions of the matrix in the warm-up.

Example 1: What is the dimension of the matrix Solution : 1 x 3
Rows x Columns

Scalar multiplication: Multiplying a matrix by a number. Each element in the matrix is
multiplied by that number .

Example 2: The table shows the prices of each item.

 Shirts Jeans Sweaters Kids’ 19.00 17.50 25.00 Women’s 30.00 35.00 40.00 Men’s 25.00 35.00 44.00

a. Arrange this data in a matrix. What are the dimensions?
b. The store is giving 25% off on all items. Use scalar multiplication to find the
matrix of sale prices.
c. In the new matrix, where can you find the sale price for women’s sweaters?

Solution :

a.

 Shirts Jeans Sweaters Kids’ Women’s Men’s

b. 25% off. The customer will pay 75% off the original price. Multiply the matrix
by 75%. Shirts Jeans Sweaters Kids’ = Women’s Men’s

c. The sale price for women’s sweaters is the second row, third column, \$30

When two matrices have the same dimensions, you can add or subtract the matrices by
adding or subtracting the elements in corresponding positions.

Example 3: Use the matrices a. Find C + D
b. Find 2C – D

Solution : C is 2 x 3 and D is 2 x 3 so the matrices can be added or subtracted. Why can’t you add or subtract matrices with different dimensions ?
Because they don’t have the same number of elements.

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