12. Find the transition matrix from the basis B to the basis c where B t and C (0.(0) for R2. In
other words find the matrix P with the property that for all UE R2, P(v B Uc. 13 Find the matrix
representation with respect to the ordered basis 11, z, T2 H, of the linear transformation S P2 P2
defined by S f(z)) a 1. Jo f(t) dt. 14. Find all real values of z for which (zI A) fails to be invertible
if 0 -1 3 A 1 0 2 15. Suppose that T V V is diagonalizable. Explain why the composite To T V V
is also diagonalizable. What are the eigenvalues of To T?
Solution
12.
12. Find the transition matrix from the basis B to the basis c where .pdf
1. 12. Find the transition matrix from the basis B to the basis c where B t and C (0.(0) for R2. In
other words find the matrix P with the property that for all UE R2, P(v B Uc. 13 Find the matrix
representation with respect to the ordered basis 11, z, T2 H, of the linear transformation S P2 P2
defined by S f(z)) a 1. Jo f(t) dt. 14. Find all real values of z for which (zI A) fails to be invertible
if 0 -1 3 A 1 0 2 15. Suppose that T V V is diagonalizable. Explain why the composite To T V V
is also diagonalizable. What are the eigenvalues of To T?
Solution
12
