Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.4 - The Algebra of Matrices - 10.4 Exercises - Page 720: 2

Answer

a. columns, rows b. BA and AA are defined.

Work Step by Step

If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix (so the number of columns of $A$ is the same as the number of rows of $B$), then the matrix product $AB$ is the $m\times k$ matrix whose $ij$-entry is the inner product of the $i\mathrm{t}\mathrm{h}$ row of $A$ and the jth column of $B.$ --- a. Fill the blanks with: ... {\bf columns} ...in the first matrix ... {\bf rows} ...in the second matrix . b. $AB$ is 3$\times\color{blue}{3}$ multiplied with a $\color{blue}{4}\times$3 ... not possible. $BA$ is $4\times\color{blue}{3}$ multiplied with a $\color{blue}{3}\times$3 ... possible $AA$ is $3\times\color{blue}{3}$ multiplied with a $\color{blue}{3}\times$3 ... possible $BA$ is $4\times\color{blue}{3}$ multiplied with a $\color{blue}{4}\times$3 ... not possible. BA and AA are defined
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