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: 14

Answer

$P=\left[\begin{array}{ll} 1 & 2\\ 7 & 6 \end{array}\right]$

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 $B.$ --- The first matrix is a 2$\times\color{blue}{3}$ matrix, and the second is a $\color{blue}{3} \times$2 matrix. So, the product is defined, and it is a 2$\times$2 matrix. Naming the product matrix $P=[p_{ij}],$ $p_{11}$ = (row 1 in A) times (column 1 in B)$=2(1)+1(3)+2(-2)=1$ $p_{12}$ = (row 1 in A) times (column $2$ in B)$=2(-2)+1(6)+2(0)=2$ $p_{21}$ = (row $2$ in A) times (column 1 in B)$=6(1)+3(3)+4(-2)=7$ $p_{22}$ = (row $2$ in A) times (column $2$ in B)$=6(-2)+3(6)+4(0)=6$ $P=\left[\begin{array}{ll} 1 & 2\\ 7 & 6 \end{array}\right]$
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