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