AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

AP EAMCET Mathematics: Matrices - Multiple Choice Questions

1. 21. Which of the following is a scalar matrix?

   • (A) Diagonal matrix with equal diagonal entries
   • (B) Zero matrix
   • (C) Identity matrix
   • (D) Diagonal matrix with different diagonal entries

   Answer: (A) Diagonal matrix with equal diagonal entries

2. 22. If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), what is \( 2A \)?

   • (A) \( \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix} \)
   • (B) \( \begin{bmatrix} 1 & 4 \\ 6 & 4 \end{bmatrix} \)
   • (C) \( \begin{bmatrix} 2 & 2 \\ 3 & 8 \end{bmatrix} \)
   • (D) \( \begin{bmatrix} 2 & 4 \\ 3 & 4 \end{bmatrix} \)

   Answer: (A) \( \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix} \)

3. 23. If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), the transpose \( A^T \) is:

   • (A) \( \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \)
   • (B) \( \begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix} \)
   • (C) \( \begin{bmatrix} 1 & 4 \\ 2 & 3 \end{bmatrix} \)
   • (D) \( \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \)

   Answer: (A) \( \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \)

4. 24. What is the determinant of \( \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \)?

   • (A) -2
   • (B) 1
   • (C) -7
   • (D) 7

   Answer: (C) -7

5. 25. If a matrix is singular, its determinant is:

   • (A) 1
   • (B) 0
   • (C) -1
   • (D) Non-zero

   Answer: (B) 0

6. 26. For a system of equations to be consistent, the rank of the coefficient matrix should:

   • (A) Be less than the rank of the augmented matrix
   • (B) Equal the rank of the augmented matrix
   • (C) Be greater than the rank of the augmented matrix
   • (D) Be zero

   Answer: (B) Equal the rank of the augmented matrix

7. 27. If \( A = \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix} \), the adjoint of \( A \) is:

   • (A) \( \begin{bmatrix} 8 & -4 \\ -6 & 2 \end{bmatrix} \)
   • (B) \( \begin{bmatrix} 4 & -6 \\ -8 & 2 \end{bmatrix} \)
   • (C) \( \begin{bmatrix} 8 & -6 \\ -4 & 2 \end{bmatrix} \)
   • (D) \( \begin{bmatrix} -8 & 4 \\ 6 & -2 \end{bmatrix} \)

   Answer: (A) \( \begin{bmatrix} 8 & -4 \\ -6 & 2 \end{bmatrix} \)

8. 28. The inverse of a matrix exists if:

   • (A) The determinant is zero
   • (B) The determinant is non-zero
   • (C) It is singular
   • (D) None of the above

   Answer: (B) The determinant is non-zero

9. 29. If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), the rank of \( A \) is:

   • (A) 0
   • (B) 1
   • (C) 2
   • (D) Cannot be determined

   Answer: (C) 2

10. 30. The solution of a consistent and independent system of linear equations represents:

    • (A) A unique solution
    • (B) Infinite solutions
    • (C) No solution
    • (D) None of these

    Answer: (A) A unique solution

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