Exercises: Add, Subtract, and Multiply Matrices

Work through each section in order. Show your work where indicated.

Grade 9·20 problems·~35 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-8

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Recall / Warm-Up

Which condition is required to add matrices $A$ and $B$ ?

A and B must both be square.

A and B must have identical dimensions (same number of rows and same number of columns).

The number of columns of A must equal the number of rows of B.

A and B must have the same number of entries but can have different shapes.

Matrix $A$ is $2 \times 3$ and matrix $B$ is $3 \times 4$ . Is the product $AB$ defined, and if so, what are its dimensions?

Not defined; inner dimensions do not match.

Defined; dimensions $3 \times 3$ .

Defined; dimensions $2 \times 4$ .

Defined; dimensions $2 \times 3$ .

To compute the $(2,1)$ entry of the product $AB$ , which row and column do you use?

Row 1 of A dotted with column 2 of B

Row 2 of A dotted with column 1 of B

The entry $a_{21}$ multiplied by $b_{12}$

Row 2 of B dotted with column 1 of A

Compute $\begin{bmatrix}1 & 3\\5 & 2\end{bmatrix} + \begin{bmatrix}-2 & 4\\1 & -3\end{bmatrix}$ . Which matrix is the result?

$\begin{bmatrix}-1 & 7\\6 & -1\end{bmatrix}$

$\begin{bmatrix}3 & -1\\4 & 5\end{bmatrix}$

$\begin{bmatrix}-2 & 12\\5 & -6\end{bmatrix}$

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

Compute $\begin{bmatrix}4 & -1\\3 & 7\end{bmatrix} - \begin{bmatrix}2 & 3\\-1 & 4\end{bmatrix}$ . What is the $(2,1)$ entry of the result?

Matrix $A$ is $3 \times 2$ and matrix $B$ is $2 \times 5$ . What are the dimensions of $AB$ ?

$2 \times 2$

$3 \times 5$

$3 \times 2$

$5 \times 3$

Let $A = \begin{bmatrix}2 & 1\\3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}1 & 0\\2 & -1\end{bmatrix}$ . Find the $(1,1)$ entry of $AB$ .

Let $A = \begin{bmatrix}2 & 1\\3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}1 & 0\\2 & -1\end{bmatrix}$ . Find the $(2,2)$ entry of $AB$ .

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