Given that P={pmatrix} 2 & 1 \\ 5 & -3 {pmatrix} and Q={pmatrix} 4 & -8 \\ 1 & -2 {pmatrix}, Find (2P-Q).

Correct Answer is : (0109−4){pmatrix} 0 & 10 \\ 9 & -4 {pmatrix}(0910−4)

{pmatrix} -6 & 17 \\ 3 & 1 {pmatrix}

{pmatrix} -2 & 9 \\ 4 & 1 {pmatrix}

{pmatrix} 0 & -6 \\ 9 & -8 {pmatrix}

{pmatrix} 0 & 10 \\ 9 & -4 {pmatrix}

Correct Answer is : (0109−4){pmatrix} 0 & 10 \\ 9 & -4 {pmatrix}(0910−4)

Test Index

WAEC Further Mathematics 2012 Paper

Question : 14

Total: 40

Given that

P=\begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}

Q=\begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}

(2P-Q)

Solution:

Concept:

Matrix scalar multiplication followed by matrix subtraction.

Explanation:

First multiply each element of

P

by 2.

2P = 2\begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}

Now subtract

Q

element-wise.

2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}

Subtract corresponding entries.

= \begin{pmatrix} 4-4 & 2-(-8) \\ 10-1 & -6-(-2) \end{pmatrix}

= \begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}

Answer:

\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}

The correct option is D.

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