Matrix-Vector Product

Practice Questions

Linear Algebra › Matrix-Vector Product

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Rewrite the system of equations:

into a matrix vector product:

where is a 3x3 matrix and are vectors in $\mathbb{R}^3$ .

$\begin{align*}&\text{Find the matrix product }\&\begin{bmatrix}-16&16\3&19\3&-1\7&-13\end{bmatrix}\times\begin{bmatrix}-1\-20\end{bmatrix}\end{align*}$

Multiply $\begin{bmatrix} 5 &3 &-1 \ 0&6 &3 \1 &-2 &1 \end{bmatrix} \cdot \begin{bmatrix} 1\5 \-2 \end{bmatrix}$

Multiply: $\begin{bmatrix} 2 & 0& -5\ -1& 3& 1\end{bmatrix} \cdot \begin{bmatrix} 2\ 2\ 1\end{bmatrix}$

$\begin{align*}&\text{Find the product }A\times B \&\text{Where }A=\begin{bmatrix}-15&16&13&-5\10&1&6&-6\end{bmatrix}\text{ and }B=\begin{bmatrix}19\6\20\0\end{bmatrix}\end{align*}$

Let $A = \begin{bmatrix} 2\sqrt{2} & \sqrt{3} \ - \sqrt{2} & 2\sqrt{3} \end{bmatrix}$ and $B = \begin{bmatrix} \sqrt{2} \ \sqrt{3} \end{bmatrix}$ .

Find .

$\begin{align*}&\text{Find the matrix product }\&\begin{bmatrix}9&-11\14&-3\end{bmatrix}\times\begin{bmatrix}7\11\end{bmatrix}\end{align*}$

Let be a matrix and $\bf{x}$ be a vector defined by

$A = \begin{bmatrix} -7 & 3 & 0 \ -9 & 0 & 2 \ 0 & 5 & -9 \end{bmatrix}$

$\bf{x} = \begin{bmatrix} -5 \ 4 \ 8 \ 3 \ 8\end{bmatrix}$

Find the product $A\bf{x}$ .

$\begin{align*}&\text{Find the value of }C\text{ if }C=A\times B \&\text{Where }A=\begin{bmatrix}-7&15\3&-8\end{bmatrix}\text{ and }B=\begin{bmatrix}16\4\end{bmatrix}\end{align*}$

Compute AB.

$A=\begin{bmatrix} 1&3 \2 &5 \end{bmatrix}$

$B = \begin{bmatrix} 4& 1& 3\ 6& -2&0 \end{bmatrix}$

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