Question

Let \( A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -5 \\ -2 \end{bmatrix}, C = [9 \ \ 7], \) which of the following is defined?

• A. Only AB
• B. Only AC
• C. Only BA
• D. All AB, AC and BA

Hint:

When multiplying matrices, make sure the number of columns in the first matrix equals the number of rows in the second matrix.

Answer 1

The Correct Option is A

Matrix multiplication is possible only if the column count of the initial matrix matches the row count of the subsequent matrix. - Given \( A \) (3x3) and \( B \) (2x1), \( AB \) is undefined. - Given \( A \) (3x3) and \( C \) (1x3), \( AC \) is undefined. - Given \( B \) (2x1) and \( A \) (3x3), \( BA \) is defined.