 # 2.9.2 Matrices, SPM Paper (Short Questions)

2.9.2 Matrices, SPM Practice (Short Questions)
Question 5:
Given that     find the value of x.

Solution:
[3 × x + x (–1)] = (18)
3xx = 18
2x = 18
x = 9

Question 6:
$\left(\begin{array}{cc}3& 4\\ -2& 3\end{array}\right)\left(\begin{array}{l}5\\ -2\end{array}\right)=$

Solution:
$\begin{array}{l}\left(\begin{array}{cc}3& 4\\ -2& 3\end{array}\right)\left(\begin{array}{l}5\\ -2\end{array}\right)=\left(\begin{array}{l}\left(3\right)\left(5\right)+\left(4\right)\left(-2\right)\\ \left(-2\right)\left(5\right)+\left(3\right)\left(-2\right)\end{array}\right)\\ \text{}=\left(\begin{array}{l}15-8\\ -10-6\end{array}\right)\\ \text{}=\left(\begin{array}{l}7\\ -16\end{array}\right)\end{array}$

Question 7:
$\left(\begin{array}{cc}2& 4\\ \begin{array}{l}-3\\ 4\end{array}& \begin{array}{l}0\\ 1\end{array}\end{array}\right)\left(\begin{array}{l}1\\ -3\end{array}\right)=$

Solution:
Order of the product of the two matrices
$=\left(\overline{)3}×2\right)\left(2×\overline{)1}\right)=\left(\overline{)3×1}\right)$

$\begin{array}{l}\left(\begin{array}{cc}2& 4\\ \begin{array}{l}-3\\ 4\end{array}& \begin{array}{l}0\\ 1\end{array}\end{array}\right)\left(\begin{array}{l}1\\ -3\end{array}\right)=\left(\begin{array}{l}2\left(1\right)+4\left(-3\right)\\ \left(-3\right)\left(1\right)+0\left(-3\right)\\ \left(4\right)\left(1\right)+1\left(-3\right)\end{array}\right)\\ \text{}=\left(\begin{array}{l}2-12\\ -3+0\\ 4-3\end{array}\right)\\ \text{}=\left(\begin{array}{l}-10\\ -3\\ 1\end{array}\right)\end{array}$

Question 8:

Solution:
Order of the product of the two matrices
$=\left(\overline{)1}×3\right)\left(3×\overline{)2}\right)=\left(\overline{)1×2}\right)$

= (1×5 + (–1)(–3) + (2)(2)  1×1 + (–1)(0) + (2)(4))
= (5 + 3 + 4   1 + 0 + 8)
= (12   9)