Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 933: 53

Answer

The coding matrix is $\left[ \begin{matrix} 14 & 4 & -18 \\ 85 & 18 & 19 \\ -33 & -7 & -9 \\ \end{matrix} \right]$.

Work Step by Step

Consider the given expression: $ SEND\_CASH $ Where, $ S=19,E=5,N=14,D=4,\_=0,C=3,A=1,S=19,H=8$ Using the cryptogram method we get, $\begin{align} & A=\left[ \begin{matrix} 1 & -1 & 0 \\ 3 & 0 & 2 \\ -1 & 0 & -1 \\ \end{matrix} \right]\left[ \begin{matrix} 19 & 4 & 1 \\ 5 & 0 & 19 \\ 14 & 3 & 8 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 19-5+0 & 4+0+0 & 1-19+0 \\ 57+0+28 & 12+0+6 & 3+0+16 \\ -19+0-14 & -4+0-3 & -1+0-8 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 14 & 4 & -18 \\ 85 & 18 & 19 \\ -33 & -7 & -9 \\ \end{matrix} \right] \end{align}$ Therefore, coding matrix of the expression is $\left[ \begin{matrix} 14 & 4 & -18 \\ 85 & 18 & 19 \\ -33 & -7 & -9 \\ \end{matrix} \right]$.
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