Math 205B Quiz 06 page 1 11/06/2009 Name
1. Find the determinant of the following matrix by hand, showing all your steps (intermediate results) along the way.
Make good use of 0’s.
4 0 8 2
0 0 4 0
10 5 7 9
3 1 6 0
2. Suppose U=
4−5 8
0 3 4
0 0 7
Suppose the following elementary row operations turn some matrix Ainto U:
Step one: rows 1 and 3 of Aare swapped,
Step two: in the matrix resulting from step one, the second row is multiplied by 6
Step three: in the matrix that results from step two, twice the third row is added to the second row.
Find det(A) and show all your work.
3A. Find the eigenvalues of C=−59 84
−42 60 ; show all your work.
3B. One of your eigenvalues λshould be positive. Find all the corresponding eigenvectors for this λ. Verify that one of
them indeed satisfies Cx=λx(choose an easy x).