Question

Assume that t is a linear transformation. Find the standard matrix of t. t: , first performs a horizontal shear that transforms into (leaving unchanged) and then reflects points through the line .

Answer 1

To find the standard matrix of the linear transformation, we need to consider the horizontal shear and reflection operations individually and then combine the resulting matrices.

Step-by-step explanation:

To find the standard matrix of the linear transformation, we need to consider the two transformation operations individually and then combine the resulting matrices. First, for the horizontal shear that transforms a into b, the standard matrix is:

[1 0]

Then, for the reflection through the line l, the standard matrix is:

[cos(2θ) sin(2θ)] [sin(2θ) -cos(2θ)]

Finally, to get the standard matrix of the overall transformation, we multiply the two matrices:

[cos(2θ) sin(2θ)] [sin(2θ) -cos(2θ)] [1 0]