Question

Use technology to compute the product.

$\left[\begin{array}{cccc}1& 7& 8& 9\\ 1& 2& 9& 1\\ 1& 5& 1& 5\\ 1& 6& 4& 8\end{array}\right]\left[\begin{array}{c}1\\ 9\\ 5\\ 6\end{array}\right]$

Short answer

The product of $\left[\begin{array}{cccc}1& 7& 8& 9\\ 1& 2& 9& 1\\ 1& 5& 1& 5\\ 1& 6& 4& 8\end{array}\right]\left[\begin{array}{c}1\\ 9\\ 5\\ 6\end{array}\right]$ is $\left[\begin{array}{c}158\\ 70\\ 81\\ 123\end{array}\right]$.

Step-by-step solution

Consider the given matrices

IfA is an $\mathit{n}\mathbf{}\mathbf{\times }\mathbf{}\mathit{m}$ matrix with row vectors $\overrightarrow{{\mathbf{\omega }}_{\mathbf{1}}}\mathbf{,}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\overrightarrow{{\mathbf{\omega }}_{\mathbf{n}}}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\overrightarrow{\mathbf{x}}$ is a vector in ${\mathit{R}}^{\mathbf{m}}$ then,

$\mathit{A}\overrightarrow{\mathbf{x}}\mathbf{=}\left[\begin{array}{c}-\overrightarrow{{\omega }_1}-\\ ⋮\\ -\overrightarrow{{\omega }_n}-\end{array}\right]\overrightarrow{\mathbf{x}}\mathbf{=}\left[\begin{array}{c}-\overrightarrow{{\omega }_1}.\overrightarrow{X}-\\ ⋮\\ -\overrightarrow{{\omega }_n}.\overrightarrow{X}-\end{array}\right]$

The given expression is,

$\left[\begin{array}{cccc}1& 7& 8& 9\\ 1& 2& 9& 1\\ 1& 5& 1& 5\\ 1& 6& 4& 8\end{array}\right]\left[\begin{array}{c}1\\ 9\\ 5\\ 6\end{array}\right]$

Here A is $\left[\begin{array}{cccc}1& 7& 8& 9\\ 1& 2& 9& 1\\ 1& 5& 1& 5\\ 1& 6& 4& 8\end{array}\right]$and $\overrightarrow{x}is\left[\begin{array}{c}1\\ 9\\ 5\\ 6\end{array}\right]$.

Find the product

By using CAS, find the product of the given matrix.

$\left[\begin{array}{cccc}1& 7& 8& 9\\ 1& 2& 9& 1\\ 1& 5& 1& 5\\ 1& 6& 4& 8\end{array}\right]\left[\begin{array}{c}1\\ 9\\ 5\\ 6\end{array}\right]=\left[\begin{array}{c}158\\ 70\\ 81\\ 123\end{array}\right]$

Hence, the product is $\left[\begin{array}{c}158\\ 70\\ 81\\ 123\end{array}\right]$.