If r={2}{-5} and s={-2}{5}, calculate 2 r-3 s.

Correct Answer is : (10−25)\;\; {10}{-25}(−2510)

Correct Answer is : (10−25)\;\; {10}{-25}(−2510)

Test Index

BECE Mathematics 2011 Paper

Question : 30

Total: 40

r=\binom{2}{-5}

s=\binom{-2}{5}

2 r-3 s

Solution:

Concept:

Vector arithmetic involves scalar multiplication and subtraction component-wise.

Explanation:

Given

r=\begin{pmatrix}2\\-5\end{pmatrix}

and

s=\begin{pmatrix}-2\\5\end{pmatrix}

First, multiply each vector by its scalar:

2r = 2\begin{pmatrix}2\\-5\end{pmatrix} = \begin{pmatrix}4\\-10\end{pmatrix}

3s = 3\begin{pmatrix}-2\\5\end{pmatrix} = \begin{pmatrix}-6\\15\end{pmatrix}

Now subtract:

2r - 3s = \begin{pmatrix}4\\-10\end{pmatrix} - \begin{pmatrix}-6\\15\end{pmatrix}

Subtract corresponding components:

= \begin{pmatrix}4-(-6)\\-10-15\end{pmatrix} = \begin{pmatrix}10\\-25\end{pmatrix}

Answer:

2r-3s = \binom{10}{-25}

, which is option C.

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