Determinants

Find matrix B, giving the elements of B in terms of p where appropriate.

Find A¹

Find AC

23

Given that the determinant of matrix B¹ is

find matrix B^–1

Give the elements of this matrix as numbers.

Show all your working.

Find 4A 2B

Find AC

Find

A B

5A + 2B

B¹

Triangle A and triangle B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B

Triangle A is transformed to triangle C under an enlargement with scale factor 3 and centre of enlargement (6, 2)

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under a reflection in the line with equation y = 3

On the grid, draw and label triangle D

Triangle B is transformed to triangle E under the transformation with matrix P where

Triangle E is transformed to triangle F under the transformation with matrix Q where

Triangle F is the image of triangle B under the matrix N

Given that the determinant of N is 2

find the coordinates of the vertices of triangle F

a b Determinant of matrix ad bc

Turn over for a spare grid if you need to redraw your triangles.

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

22

find the value of x

The determinant of matrix A is equal to the determinant of matrix B

Show that k is a root of the equation

Given that f(k) = 2k³ + 5k² – 28k – 15

use the factor theorem to show that (k + 5) is a factor of f(k)

Hence, factorise completely f(k)

The transformation with matrix C, where C is a 22 matrix, is equivalent to the transformation with matrix A followed by the transformation with matrix B

Given that k is positive,

find matrix C

Given that the determinant of matrix M is 0.5

find the value of x.

Find the matrix B.