Given that (P = begin{pmatrix} -2 & 1 \ 3 & 4 end{pmatrix}) and (Q = begin{pmatrix} 5 & -3 \ 2 & -1 end{pmatrix}), find PQ – QP.
-
A.
(begin{pmatrix} 0 & 0 \ 0 & 0 end{pmatrix}) -
B.
(begin{pmatrix} 27 & 12 \ 16 & -15 end{pmatrix}) -
C.
(begin{pmatrix} -20 & -6 \ 12 & -8 end{pmatrix}) -
D.
(begin{pmatrix} 11 & 12 \ 30 & -11 end{pmatrix})
Correct Answer: Option D
Explanation
(P = begin{pmatrix} -2 & 1 \ 3 & 4 end{pmatrix}; Q = begin{pmatrix} 5 & -3 \ 2 & -1 end{pmatrix})
= (PQ = begin{pmatrix} -10+2 & 6-1 \ 15+8 & -9-4 end{pmatrix})
= (begin{pmatrix} -8 & 5 \ 23 & -13 end{pmatrix})
(QP = begin{pmatrix} -10-9 & 5-12 \ -4-3 & 2-4 end{pmatrix})
= (begin{pmatrix} -19 & -7 \ -7 & -2 end{pmatrix})
(PQ – QP = begin{pmatrix} -8 & 5 \ 23 & -13 end{pmatrix} – begin{pmatrix} -19 & -7 \ -7 & -2 end{pmatrix})
= (begin{pmatrix} 11 & 12 \ 30 & -11 end{pmatrix})