Question

If $[A]_{3 \times 2} [B]_{x \times y} = [C]_{3 \times 1}$, then $x$ and $y$ are:

• A. $x = 1, y = 3$
• B. $x = 2, y = 1$
• C. $x = 3, y = 3$
• D. $x = 3, y = 1$

Answer 1

Answer: (B)

$x = 2, y = 1$

Answer 2

Given the matrices:

$[A]_{3 \times 2}, \quad [B]_{x \times y}, \quad [C]_{3 \times 1}.$

For matrix multiplication $[A][B]$ to be defined, the number of columns of $A$ must equal the number of rows of $B$, so:

$x = 2.$

The resulting product $[A][B]$ will have dimensions $3 \times y$, which must match $[C]_{3 \times 1}$, so:

$y = 1.$

Thus:

$x = 2, \quad y = 1.$

The correct option is:

$x = 2, \, y = 1.$