Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.1 Exercises - Page 103: 18

Answer

The first two columns of $AB$ will be equal.

Work Step by Step

Assuming that $AB$ is defined (i.e., that $A$ is an $m\times p$ matrix and $B$ is a $p\times n$ matrix), the definition of matrix multiplication gives $AB=\begin{bmatrix}A\vec{b}_{1}&A\vec{b}_{2}&\cdots&A\vec{b}_{n}\end{bmatrix}$. Since $\vec{b}_{1}=\vec{b}_{2}$ (i.e., the first two columns of $B$ are equal), it must also be that $A\vec{b}_{1}=A\vec{b}_{2}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.