English | Español

Try our Free Online Math Solver!

Online Math Solver

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


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