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IGCSE Math B5 MatricesTopic Practice

5 Matrices

Edexcel IGCSE Math B 5 Matrices question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Math B practice aligned to Edexcel, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

Question 1

[Maximum number: 2]

A=(15−42−13),B=(123456).A=\begin{pmatrix}1&5&-4\\2&-1&3\end{pmatrix}, \qquad B=\begin{pmatrix}1&2\\3&4\\5&6\end{pmatrix}.

Question 1(a)

(a)

Find AB

Question 1(b)

(b)

Find BA

[ 2 ]

Question 2

Question 2(a)

(a)

Evaluate
(1−52−2734−51)(531).\begin{pmatrix}1&-5&2\\-2&7&3\\4&-5&1\end{pmatrix} \begin{pmatrix}5\\3\\1\end{pmatrix}.

[ 5 ]

Question 2(b)

(b)

Given that
A=(−15181),B=(−3−121),C=(4−2−62)A=\begin{pmatrix}-15&1\\8&1\end{pmatrix},\quad B=\begin{pmatrix}-3&-1\\2&1\end{pmatrix},\quad C=\begin{pmatrix}4&-2\\-6&2\end{pmatrix}
and A−BC=λBA-BC=\lambda B, where λ\lambda is a scalar,

find the value of λ\lambda.

[ 5 ]

Question 3

Question 3(a)

(a)

Find the inverse of the matrix (6−2−41)\left(\begin{array}{rr}6 & -2 \\ -4 & 1\end{array}\right)

[ 2 ]

Question 3(b)

(b)

Hence, or otherwise, find the value of x and the value of y that satisfy
(6−2−41)(xy)=(5−3).\begin{pmatrix}6&-2\\-4&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}5\\-3\end{pmatrix}.

[ 4 ]

Question 7

Find the determinant of the matrix
(4−356).\begin{pmatrix}4&-3\\5&6\end{pmatrix}.

Question 3

Question 3(a)

(a)

Find the inverse of the matrix
(2254).\begin{pmatrix}2&2\\5&4\end{pmatrix}.

[ 2 ]

Question 3(b)

(b)

Use your answer to part (a) to find the value of x and the values of y that satisfy
(2254)(y2−9xx)=(0−2).\begin{pmatrix}2&2\\5&4\end{pmatrix} \begin{pmatrix}y^2-9x\\x\end{pmatrix} = \begin{pmatrix}0\\-2\end{pmatrix}.

Inverse of matrix:
(abcd)−1=1ad−bc(d−b−ca).\begin{pmatrix}a&b\\c&d\end{pmatrix}^{-1} =\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}.

[ 6 ]

Question 7

Given that A=(4−286)\mathbf{A}=\left(\begin{array}{rr}4 & -2 \\ 8 & 6\end{array}\right)
find the inverse of A

Question 4

Given that x>0 and that

(−12−3−45−6)(7−1xzx2x+2y−y)=(11−4−373−2211−524)\left(\begin{array}{rr} -1 & 2 \\ -3 & -4 \\ 5 & -6 \end{array}\right)\left(\begin{array}{ccc} 7 & -1 & x z \\ x^{2} & x+2 y & -y \end{array}\right)=\left(\begin{array}{rrr} 1 & 1 & -4 \\ -37 & 3 & -22 \\ 11 & -5 & 24 \end{array}\right)

find the value of x, the value of y and the value of z.

Question 4(e)

[Maximum number: 3]
Question image

Triangle A is drawn on the grid opposite.
The points (1,2), (3,-2) and (1,4) are the vertices of triangle B.

Question image

Triangle C is the image of triangle D under the transformation with matrix N.
Find the matrix N.

Only use this grid if you need to redraw your triangles.

Question 12

12A=(3022−1301−2)B=(43210−2)12 \quad \mathbf{A}=\left(\begin{array}{rrr}3 & 0 & 2 \\ 2 & -1 & 3 \\ 0 & 1 & -2\end{array}\right) \quad \mathbf{B}=\left(\begin{array}{rr}4 & 3 \\ 2 & 1 \\ 0 & -2\end{array}\right)
Calculate the matrix product AB.

Question 5

[Maximum number: 5]
Question image

The points with coordinates (3,1),(4,3),(6,3) and (6,1) are the vertices of a quadrilateral Q.

Question 5(c)

(a)

Quadrilateral S is the image of quadrilateral R under the transformation given by the matrix
L=(0−110).L=\begin{pmatrix}0&-1\\1&0\end{pmatrix}.

On the grid, draw and label quadrilateral S.

[ 3 ]

Question 5(d)

(b)

Find the matrix that represents the transformation that maps quadrilateral S onto quadrilateral Q.

[ 2 ]
0 selected