Exam Questions & Step-by-Step Markschemes (5 Problems)
Question 1 • 2023
3 Marks
Find the matrix X such that: 2X + \begin{pmatrix} 3 & -1 \\ 0 & 4 \end{pmatrix} = \begin{pmatrix} 7 & 5 \\ 2 & -2 \end{pmatrix}
Answer: X = \begin{pmatrix} 2 & 3 \\ 1 & -3 \end{pmatrix}
Question 2 • 2023
4 Marks
Given the matrix A = \begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix} and I is the 2 \times 2 identity matrix. (i) Find A^2 . (ii) Hence, find the scalar matrix M such that A^2 - 6A + 11I = M .
Answer: (i) \; A^2 = \begin{pmatrix} 1 & -6 \\ 18 & 13 \end{pmatrix}, \quad (ii) \; M = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} = \mathbf{O}
Question 3 • 2023
4 Marks
Given A = \begin{pmatrix} 2 & 0 \\ -1 & 7 \end{pmatrix} and I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} , find A^2 - 9A + 14I .
Answer: O = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}
Question 4 • 2024
4 Marks
Find a 2 \times 2 matrix X such that: X \begin{pmatrix} 2 & 1 \\ -3 & 4 \end{pmatrix} = \begin{pmatrix} 7 & 6 \\ 2 & 9 \end{pmatrix}
Answer: X = \frac{1}{11}\begin{pmatrix} 46 & 5 \\ 35 & 16 \end{pmatrix} = \begin{pmatrix} 46/11 & 5/11 \\ 35/11 & 16/11 \end{pmatrix}
Question 5 • 2023
3 Marks
Given A = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} and B = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix} . Find a 2 \times 2 matrix X such that AX = B .
Answer: X = \begin{bmatrix} 1 & 2 \\ 0 & 0 \end{bmatrix}