Find the standard matrix of the linear transformation T

linear-tranformation
standard-matrix

#1

Find the standard matrix of the linear transformation T.
T: ℛ2 -> ℛ2 first performs a vertical shear that maps e1 into e1 + 3e2, but leaves the vector e2 unchanged, then reflects the result through the horizontal x1-axis.

Answer:

The matrices for the two operations are A = [1 0, 0 -1] and B = [1 3, 0 1 ]. To get the matrix of T multiply AB to get [1 -3, 0 -1].