Question

given matrix a and matrix b, as shown below, what are the dimensions of ab?
a = 2 -1 4

b = \

$$\begin{bmatrix}-6 & 1 \\\\ 3 & 5 \\\\ 0 & -2\\end{bmatrix}$$

\bigcirc\\ 1 \times 3
\bigcirc\\ 3 \times 1
\bigcirc\\ 3 \times 3
\bigcirc\\ 1 \times 2
\bigcirc\\ matrix multiplication is undefined for ab.

Explanation:

Step1: Determine dimensions of A and B

Matrix \( A \) is \( 1 \times 3 \) (1 row, 3 columns). Matrix \( B \) is \( 3 \times 2 \) (3 rows, 2 columns).

Step2: Check matrix multiplication rule

For \( AB \), the number of columns in \( A \) (3) must equal the number of rows in \( B \) (3), so multiplication is defined. The resulting dimensions are rows of \( A \) (1) × columns of \( B \) (2), so \( 1 \times 2 \).

Answer:

\( 1 \times 2 \) (corresponding to the option "1 × 2")