Question Bank | Matrices | LGCSE Mathematics

180.

a = (\begin{matrix} 12 \\ - 5 \end{matrix})

and

b = (\begin{matrix} \frac{5}{2} \\ 3 \end{matrix})

Find

(a)

a + 2 b

......................... [2]

(b)

| a |

......................... [2]

Paper 1

181.

(a) (i) State the order of matrix

(\begin{matrix} 2 & 0 & - 3 \end{matrix})

.

(ii) Given that

(\begin{matrix} 2 & 4 \\ a & 3 \end{matrix}) + k (\begin{matrix} 3 & 1 \\ 0 & - 2 \end{matrix}) = (\begin{matrix} 8 & 6 \\ - 3 & - 1 \end{matrix})

.

Find the values of

a

and

k

.

(a)(i) ......................... [2] (a)(ii) a = ......................... k = ......................... [2]

Paper 1

182.

(a) Given that

A = (\begin{matrix} 2 & 3 \\ 1 & 4 \end{matrix})

and

B = (\begin{matrix} 1 & - 2 \\ 1 & 1 \end{matrix})

, find

2 A - B

.

(b) If

(\begin{matrix} k \\ 3 \end{matrix}) + (\begin{matrix} - 2 \\ p \end{matrix}) = (\begin{matrix} 4 \\ 7 \end{matrix})

, find

k

and

p

.

(a) ............................................................................ [0] k = ............................................................................ [0] p = ............................................................................ [2]

Paper 1

183.

A = (\begin{matrix} 2 & 0 \\ 3 & 1 \end{matrix})

,

B = (\begin{matrix} 1 & 2 \\ - 1 & 3 \end{matrix})

(a) Find

A - 2 B

(b) Given that

A (\begin{matrix} x \\ 2 \end{matrix}) = (\begin{matrix} 8 \\ - 2 y \end{matrix})

, find the values of

x

and

y

.

(a) ............................................................................ [1] x = ........................., y = ......................... [1]

Paper 1

184.

Vectors

\vec{A B}

and

\vec{B C}

are shown on the grid.

Find

\vec{A B} + \vec{B C}

.

................................. [2]

Paper 1

185.

The coordinates of point R are

(2, 3)

.
Find:
(a) The coordinates of point P such that R is the image of P after translation by vector

(\begin{matrix} - 5 \\ 12 \end{matrix})

......................... [2]

(b) The magnitude of

(\begin{matrix} - 5 \\ 12 \end{matrix})

......................... [2]

Paper 1

112.

(a) A =

(\begin{matrix} - 2 & 1 \\ 0 & 2 \end{matrix})

and B =

(\begin{matrix} 3 & - 1 \\ 1 & 0 \end{matrix})

(i) k A =

(\begin{matrix} 4 & - 2 \\ 0 & - 4 \end{matrix})

Find the value of k.

......................... [1]

(ii) Work out A + B

......................... [1]

(b) The coordinates of points P and Q are (-3, 1) and (5, 7) respectively.

Find

(i) The coordinates of the mid-point of PQ.

(......................... , .........................) [2]

(ii)

| \vec{P Q} |

,

......................... [3]

(iii) The equation of the line PQ.

......................... [3]

Paper 3