Find the Product of Two Matrices

Practice Questions

Pre-Calculus › Find the Product of Two Matrices

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1

We consider the matrices and that we assume of the same size .

$A=\begin{bmatrix} 34&0 &\cdots &0\ 34 &0 &\cdots &0 \\vdots &\vdots &\vdots &\vdots \ 34&0 &0 &0 \end{bmatrix},B=\begin{bmatrix} 0&2 &\cdots &0\ 0 &2&\cdots &0 \\vdots &\vdots &\vdots &\vdots \ 0&2 &0 &0 \end{bmatrix}$

Find the product .

2

$A=\begin{bmatrix} 3\ -10\ 21 \end{bmatrix}$

$B=\begin{bmatrix} 5 & 0 & -1 \ 2 & 1 & 3 \end{bmatrix}$

Find .

3

We consider the two matrices and defined below:

$A=\begin{bmatrix} 1\2 \\3 \4 \end{bmatrix}$ , $B=\begin{bmatrix} 1 &0 &1 \end{bmatrix}$

What is the matrix ?

4

Let

$A=\begin{bmatrix} 1 & 1& 1&1 \ -1& -1 & -1&-1 \1 &1 &1 &1 \ -1&-1 &-1 &-1 \end{bmatrix}$ and

$B=\begin{bmatrix} -1\ 1\ -1 \1 \end{bmatrix}$

What is the matrix ?

5

We consider the matrix equality:

$\begin{bmatrix} x & 1\ 1&x\end{bmatrix}=\begin{bmatrix} x^{2}&1 \ 1&3\end{bmatrix}$

Find the that makes the matrix equality possible.

6

Multiply $\small \begin{bmatrix} 2 &-1 &4 \ 1& 0& 2\3 &1 &-3 \end{bmatrix}*\begin{bmatrix} 10\-4 \1 \end{bmatrix}$

7

$A=\begin{bmatrix} 14 & -5 & -13 \end{bmatrix}$

$B=\begin{bmatrix} 4 \ -3\ 2 \end{bmatrix}$

Find .

8

Let be the matrix defined by:

$A=\begin{bmatrix} 1 & 1\ 1& 1 \end{bmatrix}$

The value of $A^{n}$ ( the nth power of ) is:

9

We consider the matrices and below. We suppose that and are of the same size

$A=\begin{bmatrix} 1 &1 &\cdots &1 \ 1 &1 &\cdots &1 \\vdots &\vdots &\vdots &\vdots \ 1 &1 &\cdots &1 \end{bmatrix},B=\begin{bmatrix} 2 &2 &\cdots &2 \ 2 &2 &\cdots &2 \\vdots &\vdots &\vdots &\vdots \ 2&2 &\cdots &2 \end{bmatrix}$

What is the product ?

10

$A=\begin{bmatrix} -3 & 0 \ 8 & 5 \end{bmatrix}$

$B=\begin{bmatrix} 2 & 5 \ 10 & 6 \end{bmatrix}$

Find .

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