AP ECET MATHEMATICS Multiple Choice Questions (MCQs)

1. Which of the following is the order of a matrix with 3 rows and 3 columns?

• a) 2×2
• b) 3×3
• c) 2×3
• d) 1×3

Answer: b) 3×3

2. The transpose of a matrix is obtained by:

• a) Interchanging rows and columns
• b) Adding rows and columns
• c) Subtracting rows and columns
• d) Multiplying rows and columns

Answer: a) Interchanging rows and columns

3. If a matrix is equal to its transpose, then it is:

• a) Symmetric
• b) Skew-symmetric
• c) Singular
• d) Non-singular

Answer: a) Symmetric

4. What is the determinant of a 3×3 matrix?

• a) The sum of all its elements
• b) The product of its diagonal elements
• c) A scalar value derived from its elements
• d) The difference between its rows

Answer: c) A scalar value derived from its elements

5. The cofactor of an element of a matrix is:

• a) The minor of the element multiplied by -1 raised to the power of the sum of row and column indices
• b) The sum of all elements of the matrix
• c) The determinant of the matrix
• d) None of the above

Answer: a) The minor of the element multiplied by -1 raised to the power of the sum of row and column indices

6. If the determinant of a matrix is zero, then the matrix is:

• a) Non-singular
• b) Singular
• c) Identity matrix
• d) Diagonal matrix

Answer: b) Singular

7. Which of the following is the property of the determinant of a matrix?

• a) The determinant of the transpose is equal to the determinant of the original matrix
• b) The determinant of the transpose is opposite in sign to the determinant of the original matrix
• c) The determinant of the transpose is zero
• d) The determinant of the transpose is undefined

Answer: a) The determinant of the transpose is equal to the determinant of the original matrix

8. Which method is used to find the determinant of a 3×3 matrix?

• a) Laplace’s expansion
• b) Crammer’s rule
• c) Matrix inversion method
• d) Matrix multiplication

Answer: a) Laplace’s expansion

9. The adjoint of a matrix is the transpose of which matrix?

• a) Inverse matrix
• b) Cofactor matrix
• c) Identity matrix
• d) Diagonal matrix

Answer: b) Cofactor matrix

10. If a matrix is singular, it does not have:

• a) Eigenvalues
• b) A determinant
• c) An inverse
• d) A trace

Answer: c) An inverse

11. The system of linear equations can be solved using:

• a) Matrix inversion method
• b) Laplace’s expansion
• c) Singular value decomposition
• d) Eigenvalue method

Answer: a) Matrix inversion method

12. What is Crammer’s rule used for?

• a) Solving quadratic equations
• b) Solving systems of linear equations
• c) Finding determinants of matrices
• d) Inverting matrices

Answer: b) Solving systems of linear equations

13. Which of the following is true for a non-singular matrix?

• a) It does not have a determinant
• b) Its inverse exists
• c) Its determinant is zero
• d) It is a square matrix

Answer: b) Its inverse exists

14. What is the multiplicative inverse of a matrix?

• a) The matrix that when multiplied with the original matrix gives the identity matrix
• b) The matrix that when added to the original matrix gives the identity matrix
• c) The matrix that has the same determinant as the original matrix
• d) None of the above

Answer: a) The matrix that when multiplied with the original matrix gives the identity matrix

15. Which of the following matrices is skew-symmetric?

• a) A matrix whose diagonal elements are all zero and off-diagonal elements are equal in magnitude but opposite in sign
• b) A matrix with equal elements
• c) A matrix whose diagonal elements are all ones
• d) A matrix with only one non-zero element

Answer: a) A matrix whose diagonal elements are all zero and off-diagonal elements are equal in magnitude but opposite in sign