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12 Nov 2019
Let T: R^3 rightarrow R^3 be given by T(x y z): = (x + y - z x + y - z -x + y + z). (a) Show that T is a linear map, by finding the matrix A = [T] which represents it. (b) Find the eigenvalues and eigenvectors of T. (c) Check that the trace of A is the sum of these eigenvalues. (d) Give a basis of eigenvectors for ker(T). (e) Give a basis of eigenvectors for ran(T). (f) Is T diagonalisable? (g) Is T invertible?
Let T: R^3 rightarrow R^3 be given by T(x y z): = (x + y - z x + y - z -x + y + z). (a) Show that T is a linear map, by finding the matrix A = [T] which represents it. (b) Find the eigenvalues and eigenvectors of T. (c) Check that the trace of A is the sum of these eigenvalues. (d) Give a basis of eigenvectors for ker(T). (e) Give a basis of eigenvectors for ran(T). (f) Is T diagonalisable? (g) Is T invertible?
Lelia LubowitzLv2
31 Oct 2019