Given that (P = begin{pmatrix} 3 & 4 \ 2 & x end{pmatrix}; Q = begin{pmatrix} 1 & 3 \ -2 & 4 end{pmatrix}; R = begin{pmatrix} -5 & 25 \ -8 & 26 end{pmatrix}) and PQ = R, find the value of x.
-
A.
-5 -
B.
-2 -
C.
2 -
D.
5
Correct Answer: Option D
Explanation
(P = begin{pmatrix} 3 & 4 \ 2 & x end{pmatrix}; Q = begin{pmatrix} 1 & 3 \ -2 & 4 end{pmatrix}; R = begin{pmatrix} -5 & 25 \ -8 & 26 end{pmatrix})
PQ = (begin{pmatrix} 3 & 4 \ 2 & x end{pmatrix} begin{pmatrix} 1 & 3 \ -2 & 4 end{pmatrix} = begin{pmatrix} -5 & 25 \ 2 – 2x & 6 + 4x end{pmatrix} = R)
(implies 2 – 2x = -8; -2x = -8 – 2 = -10)
(6 + 4x = 26 implies 4x = 26 – 6 = 20)
(implies x = 5)