Question

four matrices are shown. $p=\begin{bmatrix}5&8&1\\ - 3&-1&4\\ -2&0&9\\-4&-9&2end{bmatrix}$, $q = 5 2 1$, $r=\begin{bmatrix}-1&0&8\\-4&-1&0end{bmatrix}$, $s=\begin{bmatrix}5&3&-1&-6\\1&0&8&0\\-2&3&0&-2end{bmatrix}$. which matrix can be multiplied by matrix $p$? matrix $p$ matrix $q$ matrix $r$ matrix $s$

Explanation:

Step1: Recall matrix - multiplication rule

For two matrices $A$ of size $m\times n$ and $B$ of size $p\times q$, the product $AB$ is defined when $n = p$. Matrix $P$ is a $4\times3$ matrix.

Step2: Analyze the dimensions of each matrix

Matrix $Q$ is a $1\times3$ matrix, matrix $R$ is a $2\times3$ matrix, matrix $S$ is a $3\times4$ matrix. For the product $PQ$, since $P$ is $4\times3$ and $Q$ is $1\times3$, the number of columns in $P$ (3) does not match the number of rows in $Q$ (1), so $PQ$ is not defined. For $PR$, the number of columns in $P$ (3) does not match the number of rows in $R$ (2), so $PR$ is not defined. For $PS$, since the number of columns in $P$ (3) matches the number of rows in $S$ (3), the product $PS$ is defined.

Answer:

Matrix $S$