If (begin{pmatrix} 2 & 1 \ 4 & 3 end{pmatrix})(begin{pmatrix} 5 \ 4 end{pmatrix}) = k(begin{pmatrix} 17.5 \ 40.0 end{pmatrix}), find the value of k.
-
A.
1.2 -
B.
3.6 -
C.
0.8 -
D.
0.5
Correct Answer: Option C
Explanation
(begin{pmatrix} 2 & 1 \ 4 & 3 end{pmatrix})(begin{pmatrix} 5 \ 4 end{pmatrix}) = k(begin{pmatrix} 17.5 \ 40.0 end{pmatrix})
(begin{pmatrix} 10 + 4 \ 20 + 12end{pmatrix}) = (begin{pmatrix} 14 \ 32end{pmatrix}) = k(begin{pmatrix} 17.5 \ 40.0 end{pmatrix})
k = (frac{14}{17.5} = frac{32}{40} = 0.8)