UniGeniusA-level Further Maths · Edexcel 9FM0

CP 3.1, CP 3.2

Matrix arithmetic, identity and zero

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

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

and

\mathbf{B} = \begin{pmatrix} 1 & 5 \\ -2 & 0 \end{pmatrix}

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} 2 & 0 \\ -3 & 1 \end{pmatrix}

and

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

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} -2 & 5 \\ 1 & -1 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 3 & 1 \\ 2 & 2 \end{pmatrix}

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 2 & 1 \\ 0 & -1 \\ 1 & 4 \end{pmatrix}

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} 2 & -1 & 0 \\ 1 & 1 & 3 \\ 0 & 2 & -2 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 1 \\ 4 \\ -1 \end{pmatrix}

.

[3]

3 marksCore techniqueShow full working

Find

\mathbf{A}\mathbf{B}

, where

\mathbf{A} = \begin{pmatrix} 1 & -2 & 3 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 2 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 3 & -1 \end{pmatrix}

.

[3]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 2 & k \\ 1 & 3 \end{pmatrix}

.

(a)

Given that the top-left entry of

\mathbf{A}^2

is

10

, find

k

.

[2]

(b)

Hence find

\mathbf{A}^2

.

[2]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 1 & k \\ 2 & -1 \end{pmatrix}

.

(a)

Given that the top-left entry of

\mathbf{A}^2

is

9

, find

k

.

[2]

(b)

Hence find

\mathbf{A}^2

.

[2]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 3 & k \\ -1 & 2 \end{pmatrix}

.

(a)

Given that the top-left entry of

\mathbf{A}^2

is

5

, find

k

.

[2]

(b)

Hence find

\mathbf{A}^2

.

[2]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}

and

\mathbf{I}

is the

2 \times 2

identity matrix.

Find the constants

p

and

q

such that

\mathbf{A}^2 = p\mathbf{A} + q\mathbf{I}

.

[4]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix}

and

\mathbf{I}

is the

2 \times 2

identity matrix.

Find the constants

p

and

q

such that

\mathbf{A}^2 = p\mathbf{A} + q\mathbf{I}

.

[4]

4 marksCore techniqueShow full working

\mathbf{A} = \begin{pmatrix} 3 & -2 \\ 1 & 0 \end{pmatrix}

and

\mathbf{I}

is the

2 \times 2

identity matrix.

Find the constants

p

and

q

such that

\mathbf{A}^2 = p\mathbf{A} + q\mathbf{I}

.

[4]