Question

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

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

\\)
\\( \circ \\ 1 \times 3 \\)
\\( \circ \\ 3 \times 1 \\)
\\( \circ \\ 3 \times 3 \\)
\\( \circ \\ 1 \times 2 \\)
\\( \circ \\) 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 condition

For \( AB \), the number of columns in \( A \) (3) must equal the number of rows in \( B \) (3), so multiplication is defined.

Step3: Determine dimensions of AB

The dimensions of \( AB \) are (rows of \( A \)) \( \times \) (columns of \( B \)), so \( 1 \times 2 \).

Answer:

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