Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 4 - Section 4.1 - Matrix Addition and Scalar Multiplication - Exercises - Page 239: 19

Answer

$\left[\begin{array}{rrr} 0 & 2 & -2\\ -2 & 0 & 4 \end{array}\right]$

Work Step by Step

$A=\left[\begin{array}{ll} 0 & -1\\ 1 & 0\\ -1 & 2 \end{array}\right], \quad B=\left[\begin{array}{ll} 0.25 & -1\\ 0 & 0.5\\ -1 & 3 \end{array}\right],\quad C=\left[\begin{array}{ll} 1 & -1\\ 1 & 1\\ -1 & -1 \end{array}\right]$. $(A^{T})_{ij}=a_{ji}$ (write columns of A as rows of $A^T$) $2A^{T}=2a_{ji}$ -------- $A^{T}=\left[\begin{array}{lll} 0 & 1 & -1\\ -1 & 0 & 2 \end{array}\right]$ $2A^{T}=\left[\begin{array}{lll} 0 & 2 & -2\\ -2 & 0 & 4 \end{array}\right]$
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