Math 205A Quiz 07 page 1 November 14, 2008 NAME
1. Suppose Ais
142
−7113
9−53
and let v=
2
2
2
and w=
2
0
2
.
1A. Is van eigenvector of A? Explain. If it is, give the eigenvalue.
1B. Is wan eigenvector of A? Explain. If it is, give the eigenvalue.
1C. Fact: One eigenvalue for Ais λ= 4. Find a basis for the corresponding eigenspace.
2. Let C="34
67
#.
2a. Find the characteristic polynomial of C.
2b. Find any real eigenvalues of Cor explain why there are none.
3. Suppose Band Dare 4 by 4 square matrices and Det(B) is 4 and Det(BD) is 8. Find each of the
following. Write “Can’t Do” if it is not possible to find the answer with the information given.
a. Det(D). b. Det(DB).
c. Det(BT). d. Det(B−1).
e. Det(3B). f. Det(B3)
g. Det(B+B)h. Det(B+D)