2.9.1 Matrices, SPM Paper (Short Questions)

Question 1:

(\begin{matrix} 1 & 4 \\ 6 & 2 \end{matrix}) + 3 (\begin{matrix} 2 & 0 \\ 4 & - 3 \end{matrix}) - (\begin{matrix} - 3 & 0 \\ - 2 & - 5 \end{matrix})

Solution:

\begin{array}{l} (\begin{matrix} 1 & 4 \\ 6 & 2 \end{matrix}) + 3 (\begin{matrix} 2 & 0 \\ 4 & - 3 \end{matrix}) - (\begin{matrix} - 3 & 0 \\ - 2 & - 5 \end{matrix}) \\ = (\begin{matrix} 1 & 4 \\ 6 & 2 \end{matrix}) + (\begin{matrix} 6 & 0 \\ 12 & - 9 \end{matrix}) - (\begin{matrix} - 3 & 0 \\ - 2 & - 5 \end{matrix}) \\ = (\begin{matrix} 7 & 4 \\ 18 & - 7 \end{matrix}) - (\begin{matrix} - 3 & 0 \\ - 2 & - 5 \end{matrix}) \\ = (\begin{matrix} 7 - (- 3) & 4 - 0 \\ 18 - (- 2) & - 7 - (- 5) \end{matrix}) \\ = (\begin{matrix} 10 & 4 \\ 20 & - 2 \end{matrix}) \end{array}

Question 2:

Find the value of m in the following matrix equation:

(\begin{matrix} 9 & - 4 \\ 5 & 0 \end{matrix}) + \frac{1}{2} (\begin{matrix} 8 & m \\ 6 & - 10 \end{matrix}) = (\begin{matrix} 13 & - 7 \\ - 2 & 1 \end{matrix})

Solution:

\begin{array}{l} (\begin{matrix} 9 & - 4 \\ 5 & 0 \end{matrix}) + \frac{1}{2} (\begin{matrix} 8 & m \\ 6 & - 10 \end{matrix}) = (\begin{matrix} 13 & - 7 \\ - 2 & 1 \end{matrix}) \\ - 4 + \frac{1}{2} m = - 7 \\ \frac{1}{2} m = - 3 \\ m = - 6 \end{array}

Question 3:

\begin{array}{l} Given \\ (\begin{array}{l} 2 x \\ 3 y \end{array}) - 4 (\begin{array}{l} - 2 \\ 3 \end{array}) = (\begin{array}{l} - 2 \\ 6 \end{array}) \\ Find the values of x and y . \end{array}

Solution:

\begin{array}{l} 2 x + 8 = - 2 \\ 2 x = - 10 \\ x = - 5 \\ 3 y - 12 = 6 \\ 3 y = 18 \\ y = 6 \end{array}

Question 4:

\begin{array}{l} Given that matrix equation 3 (6 m) + n (3 4) = (12 7), \\ find the value of m + n \end{array}

Solution:

\begin{array}{l} 3 (6 m) + n (3 4) = (12 7) \\ 18 + 3 n = 12 \\ 3 n = - 6 \\ n = - 2 \\ 3 m + 4 n = 7 \\ 3 m + 4 (- 2) = 7 \\ 3 m = 15 \\ m = 5 \\ ∴ m + n = 5 + (- 2) = 3 \end{array}