\(\begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix}\) + \(\begin{pmatrix}p & q \\ r & s\end{pmatrix}\) = \(\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}\). What is the value of r?
A. -\(\frac{1}{8}\)
B. \(\frac{3}{8}\)
C. \(\frac{5}{8}\)
D. \(\frac{1}{4}\)
Correct Answer: D
Explanation
-2p + r = 1.......(i)
2p + 3r = 0.......(ii)
r - 1 + 2p ........(iii)
2p + 3(1 + 2p) = 0
2p + 3(1 + 2p) = 0
2p + 3 + 6p = 0
3 - 8p = 0 \(\to\) 8p = 3
p = \(\frac{3}{8}\)
6 = 1 - 2 \(\frac{3}{8}\)
= 1 - \(\frac{6}{8}\)
\(\frac{8 - 6}{8}\) = \(\frac{2}{8}\)
= \(\frac{1}{4}\)
