Quiz Details
QZ-20260504-48109
Topics:
MHT CET mahematics chapter matrices
Difficulty:
Level 3 - Medium
Questions:
5
Language:
English (English)
Generated:
May 04, 2026 at 12:58 PM
Generated by:
Guest User
Instructions: Select an answer for each question and click "Check Answer" to see if you're correct. Then view the explanation to learn more!
1 What is the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \)?
Correct Answer:
C
Explanation: The determinant is calculated as (2*4) - (3*1) = 8 - 3 = 5.
Explanation: The determinant is calculated as (2*4) - (3*1) = 8 - 3 = 5.
2 If matrix A is \( \begin{pmatrix} 1 & 2 \end{pmatrix} \) and matrix B is \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} \), what is the product AB?
Correct Answer:
B
Explanation: The product of A (1x2) and B (2x1) is calculated as (1*3 + 2*4) = 3 + 8 = 11.
Explanation: The product of A (1x2) and B (2x1) is calculated as (1*3 + 2*4) = 3 + 8 = 11.
3 Which of the following matrices is the inverse of \( \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)?
Correct Answer:
B
Explanation: The inverse of matrix \( A \) is calculated using the formula \( \frac{1}{det(A)} * adj(A) \). The determinant is 10, and the adjugate matrix gives the inverse as \( \begin{pmatrix} 3/10 & -1/5 \\ -1/10 & 4/10 \end{pmatrix} \).
Explanation: The inverse of matrix \( A \) is calculated using the formula \( \frac{1}{det(A)} * adj(A) \). The determinant is 10, and the adjugate matrix gives the inverse as \( \begin{pmatrix} 3/10 & -1/5 \\ -1/10 & 4/10 \end{pmatrix} \).
4 If matrix C is \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \), what is the product of matrix C with itself?
Correct Answer:
A
Explanation: The product of the identity matrix with itself is the identity matrix, hence the result is \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).
Explanation: The product of the identity matrix with itself is the identity matrix, hence the result is \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).
5 What is the rank of the matrix \( \begin{pmatrix} 1 & 2 & 3 \\ 0 & 0 & 0 \\ 4 & 5 & 6 \end{pmatrix} \)?
Correct Answer:
C
Explanation: The rank of a matrix is the maximum number of linearly independent row vectors. In this case, the first and third rows are independent, so the rank is 2.
Explanation: The rank of a matrix is the maximum number of linearly independent row vectors. In this case, the first and third rows are independent, so the rank is 2.