## Linear Algebra and Its Applications (5th Edition)

a) $\left[ {\begin{array}{cc} -4\\ 1 \end{array} } \right]$ b) $\left[ {\begin{array}{cc} 5\\ 4 \end{array} } \right]$
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: $$u-2v= \begin{bmatrix}-1 \\ 2\end{bmatrix} + \begin{bmatrix}6 \\ 2\end{bmatrix} = \begin{bmatrix}5 \\ 4\end{bmatrix}$$