1. Given that
.
Find
(a) the possible values of x,
(b) the value of kt.
Find
(a)
(b) the determinant of A
(c) the inverse of A.
Calculate
(a) to one decimal place, the modulus of a.
(b) a-c
Given that a+kb is parallel to c,
(c) find the value of k.
4. The points (2,1), (5, 1) and (8, 4) are the vertices of a triangle T.
(a) On graph paper, using a scale of 1 cm to represent 1 unit on each axis and taking
and
, draw and label the triangle
T.
,
(b) Calculate the matrix product
.
Hence draw and label the triangle U which is the image of T under the transformation by the matrix A.
(c) Describe fully the single transformation which is represented by the matrix A.
.
The triangle V is the image of U under the single transformation represented by the matrix B.
(d) Calculate the co-ordinates of the vertices of V, and draw and label V on your diagram.
(e) Describe fully the single transformation which is represented by the matrix B.
(f) Describe fully the single transformation which is represented by the matrix product BA.
Triangle W is the image of V under the transformation represented by the matrix C.
(g) Calculate the co-ordinates of the vertices of W, and draw and label W on your diagram.
5. Given that
, find the value of
x and
y.
(a) Find
(i)
(ii)
, yhe inverse of
A.
Given that
(b) find k.
(a) Find 3A,
Given that
(b) Find (i) B
(ii) AB
Given that AB = kC,
(c) write down the value of k.
8. A triangle U has vertices at points (1, 2), (4, 2) and (1, 3).
(a) On graph paper using a scale of 1 unit to on each axis and taking
, and
, draw and label triangle
U.
The matrix
.
(b) Calculate the matrix product
.
Triangle V is the image of triangle U under the transformation given by the matrix S.
(c) Draw and label V.
Triangle V is rotated through 180 about the point (0, 0) to produce triangle W.
(d) Draw and label triangle W.
(e) Determine the matrix X, representing the single transformation which maps triangle V to triangle W.
(f) Determine the matrix Y representing the single transformation which maps triangle U to triangle W.
9. Given that
, Calculate
.
10. (a) given that
, find the value of
p, q and
r.
(b) Given that
, write down the matrix
M.
(c) Given that
, write down the matrix
N.
11.
,
.
Calculate AB.
12. The pointa A (10,5), B (15, 20) and C (15, 5) are the vertices of a triangle.
a) On graph paper, using a scale of 2 cm to represent 5 units on each axis and taking
and
, draw and label
.
The matrix
.
b) Calculate the matrix product
.
The image of
under the transformation represented bt the matrix R is
, Where
,
and
are respecttively the images of the points A, B and C.
c) Draw and label
on your diagram.
The transformation which matrix R represent is a rotation. Find
d) the area, in square unite, of
.
e) the size, in degrees, of the angle of rotation.
13. Given that
and
, Calculate,
a) MN
b) the inverse of N.
13. The points (4, 0), (3, 2) and (4, 3) are the vertices of triangle T.
a)
Om graph paper using scale of 2 cm to represent i unit on each axis and with
and
, draw and label T.
The triangle T is transformed to another triangle U under the transformation with matrix R where
.
b) Find the co-ordinates of the vertices of U.
c) Draw and label U on your diagram.
d) On your diagram, draw and label the line x+y = 4.
The triangle T is transformed to another triangle V by means of a reflection in the line x+y = 4.
e) On your diagram, draw and label triangle V.
The triangle V is transformed under translation
to give triangle W.
f) On your diagram, draw and label triangle W.
g) Describe fully the single transformation which maps triangle W omnto triangle U.
