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10 Nov 2019
2· (14 marks) Let M2,2 be the vector space of all 2 x 2 matrices with real entries. This has a basis given by 100 0'1 0'0 1 Consider the linear transformation T : M2,2 ? M2.2 sending a matrix A to EA, where E is the matrix (a) Write down the coordinate vector [CB of the matrix with respect to 3 (2 marks) (b) Find the matrix [Ts representing T in the basis B (2 marks) (c) Verify the equality T(C))B TCb (2 marks) (d) Find the eigenvalues of [Tls and bases of the corresponding eigenspaces (4 marks) (e) Find all solutions of the equation EA XA, with A E M2.2 and ? R (4 marks)
2· (14 marks) Let M2,2 be the vector space of all 2 x 2 matrices with real entries. This has a basis given by 100 0'1 0'0 1 Consider the linear transformation T : M2,2 ? M2.2 sending a matrix A to EA, where E is the matrix (a) Write down the coordinate vector [CB of the matrix with respect to 3 (2 marks) (b) Find the matrix [Ts representing T in the basis B (2 marks) (c) Verify the equality T(C))B TCb (2 marks) (d) Find the eigenvalues of [Tls and bases of the corresponding eigenspaces (4 marks) (e) Find all solutions of the equation EA XA, with A E M2.2 and ? R (4 marks)
Jamar FerryLv2
31 Mar 2019