Class CBSE Class 12 Mathematics Matrices and Determinants Q #766
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
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
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Correct Answer: A
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





  1. AB:


    A

    3
    ×
    3


    ×

    B

    3
    ×
    1




    →
    3
    =
    3

    .
    Defined.





  2. AC:


    A

    3
    ×
    3


    ×

    C

    1
    ×
    3




    →
    3
    ≠
    1

    .
    Not Defined.





  3. BA:


    B

    3
    ×
    1


    ×

    A

    3
    ×
    3




    →
    1
    ≠
    3

    .
    Not Defined.







Hence The correct option is Only AB.





AI Tutor Explanation

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Step-by-Step Solution

First, let's determine the dimensions of the matrices:

  • A is a 3x3 matrix.
  • B is a 3x1 matrix.
  • C is a 1x3 matrix.

Now, let's check which matrix multiplications are defined:

  • AB: (3x3) * (3x1). The inner dimensions match, so AB is defined and results in a 3x1 matrix.
  • AC: (3x3) * (1x3). The inner dimensions do not match, so AC is not defined.
  • BA: (3x1) * (3x3). The inner dimensions match, so BA is defined and results in a 3x3 matrix.

Therefore, only AB and BA are defined.

Correct Answer: Only AB

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply their knowledge of matrix multiplication rules to determine which of the given matrix products are defined.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, specifically checking the compatibility of matrix dimensions for multiplication.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of matrix multiplication, a core concept covered in the textbook.

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