Question

question 5 of 5
select the correct answer.
consider matrices a and b.
$a = \

$$\begin{bmatrix}-4\\\\3\\\\18\\end{bmatrix}$$

$, $b = \

$$\begin{bmatrix}3&5&-6\\\\1&2&4\\\\-8&-7&-3\\end{bmatrix}$$

$
what is the order of the product of these matrices, $ba$?
$3 \times 1$
these two matrices cannot be multiplied.
$1 \times 3$
$3 \times 3$

Explanation:

Step1: Identify matrix orders

Matrix $A$: $3 \times 1$ (3 rows, 1 column); Matrix $B$: $3 \times 3$ (3 rows, 3 columns)

Step2: Check multiplication validity

For $BA$, columns of $B$ (3) ≠ rows of $A$ (3? No, rows of $A$ is 3, columns of $B$ is 3? Wait, correction: For matrix product $X \times Y$, columns of $X$ must equal rows of $Y$. For $BA$, $B$ is $3 \times 3$, $A$ is $3 \times 1$. Columns of $B$ = 3, rows of $A$ = 3, so multiplication is valid.

Step3: Determine product order

Order of $BA$ is (rows of $B$) $\times$ (columns of $A$) = $3 \times 1$

Answer:

$3 \times 1$