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56 questions
Mathematics (Syllabus D)/Paper 1/[Legacy] Matrices
CAIEO-Level4024-o · Paper 1

[Legacy] Matrices

56 questions· page 1 of 6

Q202024 May/Jun·P112MMedium-Easy

The matrix N\mathbf{N} satisfies the equation

3N=N+5(406−2)3\mathbf{N} = \mathbf{N} + 5 \begin{pmatrix} 4 & 0 \\ 6 & -2 \end{pmatrix}

Find N\mathbf{N}.

N\mathbf{N} = ______

Similar questions
Q232024 May/Jun·P122 partsMedium-Easy
(a)

Find A−1\mathbf{A}^{-1}.

A−1\mathbf{A}^{-1} = ______

(b)

AX=(74)\mathbf{AX} = \begin{pmatrix} 7 \\ 4 \end{pmatrix}

Find X\mathbf{X}.

X\mathbf{X} = ______

Q162024 Oct/Nov·P113 partsMedium-Easy
(a)

Express as a single matrix.

2(3−124)−(13−25)2\begin{pmatrix} 3 & -1 \\ 2 & 4 \end{pmatrix} - \begin{pmatrix} 1 & 3 \\ -2 & 5 \end{pmatrix}

______

(b)(i)

Find the value of kk.

kk = ______

(b)(ii)

Find A−1\mathbf{A}^{-1}.

A−1\mathbf{A}^{-1} = ______

Q212024 Oct/Nov·P123MMedium

The inverse of a matrix A\mathbf{A} is given by

A−1=120(m7−1k)\mathbf{A}^{-1} = \frac{1}{20} \begin{pmatrix} m & 7 \\ -1 & k \end{pmatrix}

mm and kk are positive integers and m<km < k.
The determinant of matrix A\mathbf{A} is 20.

Find A\mathbf{A}.

A\mathbf{A} = ______

Similar questions
Q182023 May/Jun·P123 partsEasy
(a)

Find how many more candles are in a large gift bag than in a small gift bag.

______

(b)(i)

N=CM\mathbf{N} = \mathbf{CM}

Find matrix N\mathbf{N}.

N\mathbf{N} = ______

(b)(ii)

Explain what each element in matrix N\mathbf{N} represents.

______

Q202023 Oct/Nov·P112 partsMedium-Easy
(a)

Find A−1\mathbf{A}^{-1}.

A−1\mathbf{A}^{-1} = ______

(b)

Find AB\mathbf{AB}.

AB\mathbf{AB} = ______

Q242022 May/Jun·P113MMedium
M=(1043)N=(k014)\mathbf{M} = \begin{pmatrix} 1 & 0 \\ 4 & 3 \end{pmatrix} \quad \mathbf{N} = \begin{pmatrix} k & 0 \\ 1 & 4 \end{pmatrix}

Given that MN=NM\mathbf{MN} = \mathbf{NM}, find the value of kk.

kk = ______

Similar questions
Q212022 Oct/Nov·P112 partsMedium-Easy
(a)

Find B\mathbf{B}.

B\mathbf{B} = ______

(b)

Find A−1\mathbf{A}^{-1}.

A−1\mathbf{A}^{-1} = ______

Q232022 Oct/Nov·P123 partsEasy
(a)

Adam buys 5 cinema tickets and 4 theatre tickets.
Ben buys 7 cinema tickets and 9 theatre tickets.

Complete the matrix, X\mathbf{X}, to represent this information.

X=(________________________)AdamBen\mathbf{X} = \begin{pmatrix} \_\_\_\_\_\_ & \_\_\_\_\_\_ \\ \_\_\_\_\_\_ & \_\_\_\_\_\_ \end{pmatrix} \begin{matrix} \text{Adam} \\ \text{Ben} \end{matrix}

CinemaTheatre\begin{matrix} \text{Cinema} & \text{Theatre} \end{matrix}

(b)(i)

P=XY\mathbf{P} = \mathbf{XY}
Find the matrix P\mathbf{P}.

P\mathbf{P} = ______

(b)(ii)

Explain what the elements in matrix P\mathbf{P} represent.

______

Q242021 May/Jun·P112 partsEasy
(a)
M=(5123)N=(4−230)\mathbf{M} = \begin{pmatrix} 5 & 1 \\ 2 & 3 \end{pmatrix} \quad \mathbf{N} = \begin{pmatrix} 4 & -2 \\ 3 & 0 \end{pmatrix}

Find M−N\mathbf{M} - \mathbf{N}.

(________________________)\begin{pmatrix} \_\_\_\_\_\_ & \_\_\_\_\_\_ \\ \_\_\_\_\_\_ & \_\_\_\_\_\_ \end{pmatrix}
(b)
P=(24c−5)Q=(32−2d)PQ=(−201911)\mathbf{P} = \begin{pmatrix} 2 & 4 \\ c & -5 \end{pmatrix} \quad \mathbf{Q} = \begin{pmatrix} 3 & 2 \\ -2 & d \end{pmatrix} \quad \mathbf{PQ} = \begin{pmatrix} -2 & 0 \\ 19 & 11 \end{pmatrix}

Find the value of cc and the value of dd.

cc = ______
dd = ______