Find the Product of a Matrix and a Scalar

Practice Questions

Pre-Calculus › Find the Product of a Matrix and a Scalar

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1

$5\begin{bmatrix} a \ b \end{bmatrix} = 14\begin{bmatrix} 20 \ 12 \end{bmatrix}$

What is ?

2

If $\frac{1}{2}$\bigl(\begin{smallmatrix} 2a\4b \end{smallmatrix} \bigr)$=$\bigl(\begin{smallmatrix} 53 \ 98 \end{smallmatrix} \bigr)$$ , what is ?

3

Simplify:

$\begin{bmatrix} 13 & 4\ 71 &3 \end{bmatrix} + 4\begin{bmatrix} 5 & 3\ 11 &22 \end{bmatrix}$

4

Evaluate: $-3\begin{bmatrix} 2& 3 & 4\ 4&-5 & 10 \end{bmatrix}$

5

Find the product.

$-3\begin{bmatrix} 4& 11& 0 \ 8 & -1 & 14\ 5 & 2 & -3 \end{bmatrix}$

6

We consider the following matrix:

$A=\begin{bmatrix} 2^m & 2^m &\cdots & 2^m &2^m \2^m & 2^m &\cdots & 2^m &2^m \ \vdots &\vdots&\vdots& \vdots &\vdots\ 2^m & 2^m &\cdots & 2^m &2^m \ 2^m & 2^m &\cdots & 2^m &2^m \end{bmatrix}$

let $k= \frac{1}{2^{m-1}}$

what matrix do we get when we perform the following product:

7

We consider the matrix defined below.

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

Find the sum : $A+A+\cdots +A (n \quad times)$

8

Let be a positive integer and let be defined as below:

$A=\begin{bmatrix} n\ \ \vdots \ n \end{bmatrix}$

Find the product .

9

Compute: $2\begin{bmatrix} -3& 4 \end{bmatrix}$

10

Find 3A given:

$A=\begin{bmatrix} 2 &1 &-3 \2 &7 &-4 \end{bmatrix}$

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