Suppose T is the transformation from R2 to R2 that results f

Suppose T is the transformation from R^2 to R^2 that results from a y-shear of 3 followed by a reflection over the line y = x. Find the matrix A that induces T. A = [0 0 0 0]

Solution

A Y-shear (parallel to Y-Axis) of 3 has x’ = x and y’ = y +3x so that (x’, y’)^T = ( x, y+3x)^T = A(x,y)^T where A =

1

0

3

1

The matrix B representing reflection across the line y = x is

0

1

1

0

hen the required matrix is BA =

0

1

1

3

1	0
3	1