Given that P={pmatrix} -2 & 1 \\ 3 & 4 {pmatrix} and Q={pmatrix} 5 & -3 \\ 2 & -1 {pmatrix}, find P Q - Q.

Correct Answer is : (111230−11){pmatrix} 11 & 12 \\ 30 & -11 {pmatrix}(113012−11)

{pmatrix} 0 & 0 \\ 0 & 0 {pmatrix}

{pmatrix} 27 & 12 \\ 16 & -15 {pmatrix}

{pmatrix} -20 & -6 \\ 12 & -8 {pmatrix}

{pmatrix} 11 & 12 \\ 30 & -11 {pmatrix}

Correct Answer is : (111230−11){pmatrix} 11 & 12 \\ 30 & -11 {pmatrix}(113012−11)

Test Index

WAEC Further Mathematics 2015 Paper

Question : 8

Total: 40

Given that

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

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

P Q

Q

Solution:

Concept:

Matrix multiplication must be done in the given order, and then one matrix is subtracted from the other.

Explanation:

First calculate

PQ

PQ = \begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}\begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}

= \begin{pmatrix} (-2)(5)+(1)(2) & (-2)(-3)+(1)(-1) \\ (3)(5)+(4)(2) & (3)(-3)+(4)(-1) \end{pmatrix}

= \begin{pmatrix} -8 & 5 \\ 23 & -13 \end{pmatrix}

Next calculate

QP

QP = \begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}\begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}

= \begin{pmatrix} (5)(-2)+(-3)(3) & (5)(1)+(-3)(4) \\ (2)(-2)+(-1)(3) & (2)(1)+(-1)(4) \end{pmatrix}

= \begin{pmatrix} -19 & -7 \\ -7 & -2 \end{pmatrix}

Then subtract

QP

from

PQ

PQ - QP = \begin{pmatrix} -8 & 5 \\ 23 & -13 \end{pmatrix} - \begin{pmatrix} -19 & -7 \\ -7 & -2 \end{pmatrix}

= \begin{pmatrix} 11 & 12 \\ 30 & -11 \end{pmatrix}

Answer:

\begin{pmatrix} 11 & 12 \\ 30 & -11 \end{pmatrix}

, which is option D.

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