EXERCISE … TRANSFORMATION WITH MATRICES
1) a) Draw x- and y – axis with values from – 8 to +8.
b) Draw the triangle A(2, 2), B(6, 2) and C(6, 4). Find the image under the transformation
represented by the following matrices.
i)
0 1
1 0
(ii)
1
0
0
1
(iii)
1
0
0
- 1
(iv)
0
1
1
1
0
(v)
c) Describe a single transformation which maps:
(i) A1B1C1 onto A2B2C2
(ii) ABC onto A4B4C4
1
2
1 1
2
2) a) On a graph paper draw a triangle T whose vertices are (2, 2), (6, 2) and (6, 4).
b) Draw the axes from – 8 to +8 using a scale of 1cm to represent 1 unit on each axis.
c) Draw the image U of T under the transformation whose matrix is
d) Draw the image V of T under the transformation whose matrix is
0
1
1
0
e) Draw the image W of T under the transformation whose matrix is
f) Draw the image X of T under the transformation whose matrix is
1
0
0
-1
.
.
0 -1
1 0
1 - 3
0 1
.
.
g) Describe a single transformation which would map U onto V.
3) a) Draw L(1, 1), M(3, 3) and N(4, 1) and its image L’M’N’ under the matrix A =
b) Find and draw the image of L’M’N’ under the matrix B =
0 1
1 0
1
0
0
-1
and label it as L’’M’’N’’
c) Calculate the matrix product BA.
d) Find the image of LMN under the matrix BA, and compare with result of performing BA(LMN).
(Axes: Both axes from -5 to +5 using a scale of 1cm to 1 unit).
4) a) Draw P(0, 0), Q(2, 2) and R(4, 0) and its image P’Q’R’ under the matrix A =
b) Find and draw the image of P’Q’R’ under the matrix B =
c) Calculate the matrix product BA.
1
0
1
1
2
0
0
2
.
and label it as P’’Q’’R’’
d) Find the image of PQR under the matrix BA, and compare with result of performing BA(PQR).
(Axes: x –axis 0 to +6 and y axis 0 to +9)