Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.9 Exercises - Page 79: 18

Answer

See solution

Work Step by Step

\[ T(\mathbf{x})=\left[\begin{array}{c} 2 x_{2}-3 x_{1} \\ x_{1}-4 x_{2} \\ 0 \\ x_{2} \end{array}\right]=A\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \] To express $T(x)$ as $A x,$ write $T(x)$ and $x$ as column vectors, and then fill in the entries in $A$ by inspection \[ T(\mathbf{x})=\left[\begin{array}{cc} -3 & 2 \\ 1 & -4 \\ 0 & 0 \\ 0 & 1 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \] since $x$ has 2 entries, $A$ has 2 columns. So $T(x)$ has 4 entries, $A$ has 4 rows
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