Let T: R R be the linear transformation of the ry-plane given by a stretch with...

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Let T: R R be the linear transformation of the ry-plane given by a stretch with factor 3 along the line y = -x and a compression by along the line y = x (see Figure 1). y = x ** y=-x y=x y=-x Figure 1: The unit circle in R2 (left) and its image under T (right). (a) Find the eigenvalues of T. (b) Find the corresponding eigenspaces of T. (c) Choose a basis B of eigenvectors of T and give the matrix representation of T with respect to this basis. (d) Finally, find the standard matrix representation [T]s of T. Let T: R R be the linear transformation of the ry-plane given by a stretch with factor 3 along the line y = -x and a compression by along the line y = x (see Figure 1). y = x ** y=-x y=x y=-x Figure 1: The unit circle in R2 (left) and its image under T (right). (a) Find the eigenvalues of T. (b) Find the corresponding eigenspaces of T. (c) Choose a basis B of eigenvectors of T and give the matrix representation of T with respect to this basis. (d) Finally, find the standard matrix representation [T]s of T.

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