If (a = begin{pmatrix} 3 \ 2 end{pmatrix}) and (b = begin{pmatrix} -3 \ 5 end{pmatrix}), find a vector c such that (4a + 3c = b).
-
A.
(begin{pmatrix} 3 \ -1 end{pmatrix}) -
B.
(begin{pmatrix} -5 \ -1 end{pmatrix}) -
C.
(begin{pmatrix} -5 \ 1 end{pmatrix}) -
D.
(begin{pmatrix} -5 \ -9 end{pmatrix})
Correct Answer: Option B
Explanation
(4 begin{pmatrix} 3 \ 2 end{pmatrix} + 3 begin{pmatrix} x \ y end{pmatrix} = begin{pmatrix} -3 \ 5 end{pmatrix})
(begin{pmatrix} 12 \ 8 end{pmatrix} + begin{pmatrix} 3x \ 3y end{pmatrix} = begin{pmatrix} -3 \ 5 end{pmatrix})
(begin{pmatrix} 3x \ 3y end{pmatrix} = begin{pmatrix} -3 – 12 \ 5 – 8 end{pmatrix})
(begin{pmatrix} 3x \ 3y end{pmatrix} = begin{pmatrix} -15 \ -3 end{pmatrix})
(begin{pmatrix} x \ y end{pmatrix} = begin{pmatrix} -5 \ -1 end{pmatrix})