Matrices Quiz - CBSE Class 12 Mathematics

Free practice quiz: Matrices (CBSE Class 12 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 12 Mathematics practice quiz has 17 multiple-choice questions on Matrices, and 17 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. What is a 2x2 identity matrix?

   1. [[1, 0], [0, 1]]
   2. [[0, 1], [1, 0]]
   3. [[1, 1], [1, 1]]
   4. [[0, 0], [0, 0]]
   Show answer

   Answer: A. [[1, 0], [0, 1]]

   An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For a 2x2 matrix, it is [[1, 0], [0, 1]].

2. Find the result of multiplying the matrix [[1, 2], [3, 4]] with a 2x2 zero matrix.

   1. [[1, 2], [3, 4]]
   2. [[0, 0], [0, 0]]
   3. [[4, 6], [6, 8]]
   4. [[5, 6], [6, 7]]
   Show answer

   Answer: B. [[0, 0], [0, 0]]

   Any matrix multiplied by a zero matrix results in a zero matrix of the same size.

3. If A = [[1, 2], [3, 4]], find 2A.

   1. [[2, 4], [6, 8]]
   2. [[1, 2], [3, 4]]
   3. [[3, 6], [9, 12]]
   4. [[-1, -2], [-3, -4]]
   Show answer

   Answer: A. [[2, 4], [6, 8]]

   2A is the matrix obtained by multiplying each element of A by 2: [[2*1, 2*2], [2*3, 2*4]] = [[2, 4], [6, 8]].

4. What is the rank of a 3x3 identity matrix?

   1. 2
   2. 1
   3. 0
   4. 3
   Show answer

   Answer: D. 3

   An identity matrix has full rank equal to its dimensions; for a 3x3 identity matrix, the rank is 3.

5. Find the eigenvalues of matrix [[4, 0], [0, 6]].

   1. 4, 6
   2. 10, 0
   3. 0, 0
   4. 2, 3
   Show answer

   Answer: A. 4, 6

   For a diagonal matrix, the eigenvalues are the elements on the main diagonal.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If A = [[2, 3], [1, 4]], what is the element in the second row, first column?
2. What is the determinant of a 2x2 matrix [[a, b], [c, d]]?
3. If A = [[1, 0, 0], [0, 1, 0], [0, 0, 1]], what type of matrix is A?
4. Find the transpose of the matrix [[1, 2, 3], [4, 5, 6]].
5. Multiply the matrices: [[1, 0], [0, 1]] and [[2, 3], [4, 5]].
6. Analyze the rank of the matrix A = [[1, 2], [2, 4]].
7. Determine the inverse of the matrix [[1, 0], [0, 1]].
8. Find the determinant of matrix [[4, 3], [6, 3]].
9. Which of the following matrices is non-singular?
10. Determine if the matrix [[2, -1], [-1, 2]] is positive definite.
11. What is the trace of the matrix [[5, 1, 0], [2, 7, 2], [0, 0, 9]]?
12. Can a 3x2 matrix be orthogonal?

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