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Let T: R^2 rightarrow R^2 be the linear transformation of the xy-plane given by a stretch with factor 3 along the line y = -x and a compression by 1/2 along the line y = x(see Figure 1). (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. Show transcribed image text
Let T: R^2 rightarrow R^2 be the linear transformation of the xy-plane given by a stretch with factor 3 along the line y = -x and a compression by 1/2 along the line y = x(see Figure 1). (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.
Show transcribed image text Deanna HettingerLv2
28 Apr 2019