Question

4 0 0 17. 0 0 2 5 18. 0 0 0 0 -1 1 2 0 -3 ? If so, find the eigen- 2 3 19. For A = 1 2 3, find one eigenvalue, with no cal- 3 7 9 1 2 3 4 -5 1 ? If so, find 2 4 4 culation. Justify your answer. 6 7 2 7 ? If so, find the 6 4 20. Without calculation, find one eigenvalue and two linearly independent eigenvectors of A = 5 -5 5 5 -5 5. Justify 5 -5 5 your answer. 0 -1 3 1 ? If so, find one 4 5 In Exercises 21-30, A is an n × n matrix. Mark each statement True or False (T/F). Justify each answer. 21. (T/F) If Ax = ?x for some vector x, then ? is an eigenvalue of A. 2 2 -2 1 ? If so, find one 1 1 22. (T/F) If Ax = ?x for some scalar ?, then x is an eigenvector of A. 280

          4
0 0
17.
0
0
2
5
18.
0
0
0
0 -1
1
2
0 -3
? If so, find the eigen-
2
3
19. For A = 1
2
3, find one eigenvalue, with no cal-
3
7
9
1
2
3
4 -5
1 ? If so, find
2
4
4
culation. Justify your answer.
6
7
2
7
? If so, find the
6
4
20. Without calculation, find one eigenvalue and two linearly
independent eigenvectors of A = 
5 -5 5
5 -5 5. Justify
5 -5 5
your answer.
0 -1
3 1
? If so, find one
4 5
In Exercises 21-30, A is an n × n matrix. Mark each statement
True or False (T/F). Justify each answer.
21. (T/F) If Ax = ?x for some vector x, then ? is an eigenvalue
of A.
2 2
-2 1
? If so, find one
1 1
22. (T/F) If Ax = ?x for some scalar ?, then x is an eigenvector
of A.
280

4
0 0
17.
0
0
2
5
18.
0
0
0
0 -1
1
2
0 -3
? If so, find the eigen-
2
3
19. For A = 1
2
3, find one eigenvalue, with no cal-
3
7
9
1
2
3
4 -5
1 ? If so, find
2
4
4
culation. Justify your answer.
6
7
2
7
? If so, find the
6
4
20. Without calculation, find one eigenvalue and two linearly
independent eigenvectors of A =
5 -5 5
5 -5 5. Justify
5 -5 5
your answer.
0 -1
3 1
? If so, find one
4 5
In Exercises 21-30, A is an n × n matrix. Mark each statement
True or False (T/F). Justify each answer.
21. (T/F) If Ax = ?x for some vector x, then ? is an eigenvalue
of A.
2 2
-2 1
? If so, find one
1 1
22. (T/F) If Ax = ?x for some scalar ?, then x is an eigenvector
of A.
280

Added by Francisco Jose G.

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