J20
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a<br />
b<br />
The matrix transforms the vectors<br />
c<br />
d<br />
1 a<br />
0<br />
b<br />
→ and <br />
0<br />
c<br />
1<br />
d <br />
Example<br />
1<br />
<br />
and<br />
0<br />
0<br />
as follows<br />
1<br />
<br />
A is a reflection in the line y = x. B is a reflection in the y-axis. Find the matrix which<br />
represents:<br />
(a) A (b) B<br />
Solution<br />
(a)<br />
The images of I(1. 0) and J(0. 1) under this transformation (A) are I 1( 0, 1) and<br />
J 1 (1, 0).<br />
0<br />
1 <br />
Therefore, the matrix representing the transformation is <br />
1<br />
0<br />
(b)<br />
The images of I and J under transformation B are ! 1 (-1, 0) and J 1 (0, 1), respectively.<br />
1<br />
0<br />
Therefore, the matrix representing B is <br />
0 1 <br />
Example
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