If (V = begin{pmatrix} -2 \ 4 end{pmatrix}) and (U = begin{pmatrix} -1 \ 5 end{pmatrix}), find (|U + V|).
-
A.
(3sqrt{10}) -
B.
(sqrt{82}) -
C.
15 -
D.
(2sqrt{5})
Correct Answer: Option A
Explanation
(V = begin{pmatrix} -2 \ 4 end{pmatrix}) and (U = begin{pmatrix} -1 \ 5 end{pmatrix})
(U + V = begin{pmatrix} -1 – 2 \ 5 + 4 end{pmatrix} = begin{pmatrix} -3 \ 9 end{pmatrix})
(|U + V| = sqrt{(-3)^{2} + 9^{2}} = sqrt{9 + 81} = sqrt{90})
= (sqrt{9 times 10} = 3sqrt{10})