If (P = begin{pmatrix} 1 & 2 \ 5 & 1 end{pmatrix}) and (Q = begin{pmatrix} 0 & 1 \ 1 & 3 end{pmatrix}), find PQ.
-
A.
(begin{pmatrix} 5 & 1 \ 16 & 5 end{pmatrix}) -
B.
(begin{pmatrix} 2 & 16 \ 1 & 10 end{pmatrix}) -
C.
(begin{pmatrix} 2 & 7 \ 1 & 8 end{pmatrix}) -
D.
(begin{pmatrix} 2 & 5 \ -1 & -8 end{pmatrix})
Correct Answer: Option C
Explanation
(begin{pmatrix} 1 & 2 \ 5 & 1 end{pmatrix} begin{pmatrix} 0 & 1 \ 1 & 3 end{pmatrix})
= (begin{pmatrix} 1times 0 + 2times 1 & 1times 1 + 2times3 \ 5times0 + 1times1 & 5times1 + 1times 3 end{pmatrix})
= (begin{pmatrix} 2 & 7 \ 1 & 8 end{pmatrix})