Given that ( a = begin{pmatrix} 2 \ 3 end{pmatrix}) and (b = begin{pmatrix} -1 \ 4 end{pmatrix}), evaluate ((2a – frac{1}{4}b)).
-
A.
(begin{pmatrix} frac{17}{4} \ 7 end{pmatrix}) -
B.
(begin{pmatrix} frac{17}{4} \ 5 end{pmatrix}) -
C.
(begin{pmatrix} frac{17}{4} \ 3 end{pmatrix}) -
D.
(begin{pmatrix} frac{17}{4} \ 2 end{pmatrix})
Correct Answer: Option B
Explanation
(a = begin{pmatrix} 2 \ 3 end{pmatrix}); (b = begin{pmatrix} -1 \ 4 end{pmatrix})
(implies 2 times a = begin{pmatrix} 4 \ 6 end{pmatrix}) and (frac{1}{4} times b = begin{pmatrix} -frac{1}{4} \ 1 end{pmatrix})
(therefore 2a – frac{1}{4}b = begin{pmatrix} 4 – frac{-1}{4} \ 6 – 1 end{pmatrix})
= (begin{pmatrix} frac{17}{4} \ 5 end{pmatrix})