If u={3}{1} and v={-2}{1}, evaluate 6 v+2 u

Correct Answer is : (−68)\; \; {-6}{8}(8−6)

Correct Answer is : (−68)\; \; {-6}{8}(8−6)

Test Index

BECE Mathematics 2018 Paper

Question : 28

Total: 40

u=\binom{3}{1}

v=\binom{-2}{1}

6 v+2 u

Solution:

Concept:

Scalar multiplication and addition of column vectors are performed component-wise.

Explanation:

Given

u=\binom{3}{1}

and

v=\binom{-2}{1}

, evaluate

6v+2u

First multiply each vector by its scalar:

6v=6\binom{-2}{1}=\binom{-12}{6}

2u=2\binom{3}{1}=\binom{6}{2}

Now add the two resulting vectors component-wise:

6v+2u=\binom{-12}{6}+\binom{6}{2}

\Rightarrow 6v+2u=\binom{-12+6}{6+2}

\Rightarrow 6v+2u=\binom{-6}{8}

Answer:

\binom{-6}{8}

, which is option B.

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