Finding Scalar Multiples of a Matrix
Besides adding and subtracting whole matrices, there are many situations in which we need to multiply a matrix by a constant called a scalar. Recall that a scalar is a real number quantity that has magnitude, but not direction. For example, time, temperature, and distance are scalar quantities. The process of scalar multiplication involves multiplying each entry in a matrix by a scalar. A scalar multiple is any entry of a matrix that results from scalar multiplication. Consider a real-world scenario in which a university needs to add to its inventory of computers, computer tables, and chairs in two of the campus labs due to increased enrollment. They estimate that 15% more equipment is needed in both labs. The school’s current inventory is displayed in the table below.
Lab A | Lab B | |
---|---|---|
Computers | 15 | 27 |
Computer Tables | 16 | 34 |
Chairs | 16 | 34 |
A General Note: Scalar Multiplication
Scalar multiplication involves finding the product of a constant by each entry in the matrix. GivenExample 6: Multiplying the Matrix by a Scalar
Multiply matrix by the scalar 3.Solution
Multiply each entry in by the scalar 3.Try It 2
Given matrix find whereExample 7: Finding the Sum of Scalar Multiples
Find the sum .Solution
First, find then .Licenses & Attributions
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- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.