# 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

**Matrix Addition and Subtraction **

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.

Prev | Next |