Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - Problems: 1

Answer

a) $\left[ {\begin{array}{cc} -4\\ 1 \end{array} } \right]$ b) $\left[ {\begin{array}{cc} 5\\ 4 \end{array} } \right]$

Work Step by Step

Vector addition works by adding up components of vectors: $$u+v= \begin{bmatrix}-1 \\ 2\end{bmatrix} + \begin{bmatrix}-3 \\ -1\end{bmatrix} = \begin{bmatrix}-4 \\ 1\end{bmatrix} $$ Vector-Scalar Multiplication works by multiplying the scalar by each component of the vector: $$u-2v= \begin{bmatrix}-1 \\ 2\end{bmatrix} + \begin{bmatrix}6 \\ 2\end{bmatrix} = \begin{bmatrix}5 \\ 4\end{bmatrix} $$
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