Exercises: Multiply Matrices by Scalars

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Grade 9·18 problems·~25 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-7

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Recall / Warm-Up

If $A = \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix}$ and $c = 3$ , what is the $(1,2)$ entry of $cA$ ?

$-1$

$-3$

$3$

$6$

Matrix $A$ has dimensions $3 \times 5$ . What are the dimensions of $7A$ ?

$21 imes 35$

$3 imes 5$

$21 imes 5$

$10 imes 12$

A payoff matrix for a game is $P = \begin{bmatrix} 4 & -2 \\ 1 & 3 \end{bmatrix}$ . If all payoffs are doubled, the new payoff matrix is:

$\begin{bmatrix} 4 & -2 \\ 1 & 3 \end{bmatrix} + 2$

$\begin{bmatrix} 6 & 0 \\ 3 & 5 \end{bmatrix}$

$\begin{bmatrix} 8 & -4 \\ 2 & 6 \end{bmatrix}$

$\begin{bmatrix} 16 & 4 \\ 4 & 9 \end{bmatrix}$

Compute $-2 \begin{bmatrix} 1 & 3 \\ -4 & 0 \end{bmatrix}$ . Which matrix is the result?

$\begin{bmatrix} -2 & -6 \\ 8 & 0 \end{bmatrix}$

$\begin{bmatrix} -2 & -6 \\ -8 & 0 \end{bmatrix}$

$\begin{bmatrix} -1 & -3 \\ 4 & 0 \end{bmatrix}$

$\begin{bmatrix} 2 & 6 \\ -8 & 0 \end{bmatrix}$

Compute $4 \begin{bmatrix} 3 & -1 & 0 \\ 2 & 5 & -3 \end{bmatrix}$ . What is the entry in row 2, column 3?

For $A = \begin{bmatrix} 5 & 2 \\ -1 & 3 \end{bmatrix}$ , find the $(1,1)$ entry of $(-1)A$ (i.e., $-A$ ).

Matrix $B$ has dimensions $2 \times 4$ . Which statement about $cB$ (for any nonzero real $c$ ) is always true?

The dimensions of $cB$ depend on whether $c$ is positive or negative.

The dimensions of $cB$ are $2 \times 4$ .

The dimensions of $cB$ are the same as the dimensions of $c$ , which is $1 \times 1$ .

The dimensions of $cB$ are $2c \times 4c$ .

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