MATH 54 QUIZ 6-
1. Is λ = 1 an eigenvalue of
? If so, find one corresponding eigenvector.
2. Find a basis for the eigenspace corresponding to each listed eigenvalue: A =
, λ = 3, 7.
3. Find the characteristic polynomial of the following matrix.
![647_Figure2.png](https://secure.tutorsglobe.com/CMSImages/647_Figure2.png)
4. Diagonablize the following matrix, if possible. It has eigenvalues λ = 2, 3.
![2038_Figure3.png](https://secure.tutorsglobe.com/CMSImages/2038_Figure3.png)
5. Let B = {b1, b2, b3} be a basis for a vector space V and let T: V → R2 be a linear transformation with the property that
![587_Figure4.png](https://secure.tutorsglobe.com/CMSImages/587_Figure4.png)
Find the matrix for T relative to B and the standard basis for R2.
6. True/False (no justification required, full credit only if all 4 parts are correct)
(i) A is diagonalizable if A has n eigenvectors.
(ii) If A is diagonalizable, then A has n distinct eigenvalues.
(iii) If AP = PD, with D diagonal, then the nonzero columns of P must be eigenvectors of A.
(iv) If A is invertible, then A is diagonalizable.