Solved: Let \[ A = \begin{pmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{pmat...

ID: Class: 12 Subject: Math Topic: Matrices and Determinants Type: Mcq Year: 2025

Question:

Let \[ A = \begin{pmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} -2 \\ -5 \\ -7 \end{pmatrix}, \quad C = \begin{pmatrix} 9 & 8 & 7 \end{pmatrix}, \] which of the following is defined?

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

Official Solution

Correct Answer: Only AB

Explanation:

The problem is to determine which matrix multiplication is defined. A product of two matrices $P \times Q$ is defined if and only if the number of columns of $P$ equals the number of rows of $Q$.

The order of Matrix A is 3×3

The order of Matrix B is 3×1 and

The order of Matrix C is 1×3

Checking Products

AB:
$A_{3 \times 3} \times B_{3 \times 1}$
$\to 3 = 3$
.
Defined.

AC:
$A_{3 \times 3} \times C_{1 \times 3}$
$\to 3 \neq 1$
.
Not Defined.

BA:
$B_{3 \times 1} \times A_{3 \times 3}$
$\to 1 \neq 3$
.
Not Defined.

Hence The correct option is Only AB.

QPaperGen

Question:

Official Solution

Checking Products

AI Teacher