Linear Algebra and Its Applications, 4th Edition

Published by Brooks Cole
ISBN 10: 0030105676
ISBN 13: 978-0-03010-567-8

Chapter 1 - Section 1.4 - Matrix Notation and Matrix Multiplication - Problem Set - Page 32: 59

Answer

$v = (3,4,5)^\top$, $50$, $\texttt{Error}$

Work Step by Step

Since $A$ is the identity matrix, $Av = v$ for all vectors $v$ in $\mathbb{R}^3$. Thus, $Av = v = (3,4,5)^\top$. $v' \cdot v$ is equal to $v^\top v$. This can be expanded to get $$v^\top v = v_1^2 + v_2^2 + v_3^2= 3^2+4^2+5^2=50$$ Lastly, since $v$ is $3$ by $1$ and $A$ is $3$ by $3$, $v A$ is undefined (matrix multiplication cannot be done). Thus, you should get an error when trying to compute $vA$.
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