The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are
defined.
-$A$ is $1 \times 4 , B$ is $4 \times 1$.
A) $\mathrm { AB }$ is undefined, BA is $4 \times 4$.
B) $\mathrm { AB }$ is $4 \times 4$, BA is $1 \times 1$.
C) $\mathrm { AB }$ is $1 \times 1 , \mathrm { BA }$ is undefined.
D) $\mathrm { AB }$ is $1 \times 1$, $\mathrm { BA }$ is $4 \times 4$.

Question

Quizplus · Accepted Answer

For matrix multiplication to be defined, the number of columns in the first matrix must equal the number of rows in the second matrix. Since A is $1 \times 4$ and B is $4 \times 1$, AB is defined and results in a $1 \times 1$ matrix. Similarly, BA is defined and results in a $4 \times 4$ matrix.

The Sizes of Two Matrices a and B Are Given AAA

The Sizes of Two Matrices a and B Are Given $A$