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 defined when the number of columns in the first matrix equals the number of rows in the second matrix. - \( A \) is a 3x3 matrix, \( B \) is a 2x1 matrix, so \( AB \) is undefined. - \( A \) is a 3x3 matrix, \( C \) is a 1x3 matrix, so \( AC \) is undefined. - \( B \) is a 2x1 matrix, \( A \) is a 3x3 matrix, so \( BA \) is defined.