Name:
CSU ID:
Homework 8
March 27, 2015


16


1. Suppose that T is a linear operator. Find T  24  given that
1








−2
−1

 

T  4  =  3  ,
0
0
−7
1

 

T  1  =  2 
8
−4


2. S5.1 ]6(d), ]10
3. S5.1 ]12
4. S5.1 ]14
5. S5.1 ]20(a,c,e)
6. S5.1 ]24
7. S5.1 ]34
8. S5.1 ]36
9. The eigenvalues of A given below are λ = 3, −2, 6. Find the eigenvectors and, if possible, define them in terms of integers. Define an S
and S −1 such that S −1 AS = diag(3, −2, 6) (diag(a, b) refers to a 2 × 2
diagonal matrix with a and b on the main diagonal.)


−36 126
97


A =  12 −30 −26 
−30
90
73
*** For the problems listed below, we will know on Wednesday if they
should be turned in with homework on Friday. If not, you should still
expect S5.2 to be covered on Exam 2.
10. S5.2 ]20
11. S5.2 ]27
12. S5.2 ]32


1
−7

 

T  2  =  0 
0
−3