Write the matrix a by transforming

Reference no: EM13189166

Consider the matrix A of the linear transformation T in two dimensional space that rotates all vectors 45 degrees in the clockwise direction, and then shrinks their horizontal component by a factor of two.
a) Write the matrix A by transforming the canonical basis e1, e2 (unit vectors e1 and e2).
b) Think of T as the composition of two simpler transformations: rotation and stretching. Write the matrix for each, and check that their product equals A.
c) Describe in words the action of the transformation S which is inverse to T . Use your description of S to write its matrix B. Check that the matrix B is indeed the inverse of A.

Reference no: EM13189166

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