(begin{pmatrix} -2 & 1 \ 2 & 3 end{pmatrix}) + (begin{pmatrix}p & q \ r & send{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: Option 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})