Given that vectors u = {pmatrix} -3 \\ 5 {pmatrix} and v = {pmatrix} 2 \\ -3 {pmatrix}, calculate 2v - u

Correct Answer is : ((7−11))≤ft( {pmatrix} 7 \\ -11 {pmatrix})((7−11))

≤ft({pmatrix} 1 \\ -1 {pmatrix})

≤ft({pmatrix} -1 \\ 1 {pmatrix})

≤ft( {pmatrix} -7 \\ -11 {pmatrix})

≤ft( {pmatrix} 7 \\ -11 {pmatrix})

Correct Answer is : ((7−11))≤ft( {pmatrix} 7 \\ -11 {pmatrix})((7−11))

Test Index

BECE Mathematics 2015 Paper

Question : 33

Total: 40

Given that vectors

u = \begin{pmatrix} -3 \\ 5 \end{pmatrix}

v = \begin{pmatrix} 2 \\ -3 \end{pmatrix}

2v - u

Solution:

Concept:

Vector operations are performed component-wise, so scalar multiplication and subtraction apply separately to each row.

Explanation:

Given

u = \begin{pmatrix} -3 \\ 5 \end{pmatrix}

and

v = \begin{pmatrix} 2 \\ -3 \end{pmatrix}

First multiply

v

by the scalar

2

2v = 2 \begin{pmatrix} 2 \\ -3 \end{pmatrix} = \begin{pmatrix} 2 \times 2 \\ 2 \times (-3) \end{pmatrix} = \begin{pmatrix} 4 \\ -6 \end{pmatrix}

Now subtract

u

from

2v

2v - u = \begin{pmatrix} 4 \\ -6 \end{pmatrix} - \begin{pmatrix} -3 \\ 5 \end{pmatrix}

Subtract the corresponding components:

= \begin{pmatrix} 4 - (-3) \\ -6 - 5 \end{pmatrix}

= \begin{pmatrix} 4 + 3 \\ -11 \end{pmatrix}

= \begin{pmatrix} 7 \\ -11 \end{pmatrix}

Answer:

2v - u = \begin{pmatrix} 7 \\ -11 \end{pmatrix}

, which is option D.

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