1.
2.
3.
4.
5.
Matrix Theory HW 10. Not to be turned in.
Which of the following are Jordan matrices?
1 0 0
3 1 0
1 0
, 0 3 1 , 0 3 1 ,
0 0
0 0 3
0 0 2
1 0 0 0 0
1 1 0
0 3 1 , 0 0 2 1 0 .
0 0 0 2 0
0 0 3
0 0 0 0 0
What are the possible Jordan forms of
1.
2.
3.
4.
5.
6.
7.
Matrix Theory HW 9. Not to turn in.
Do problem 1., (a) - (f) on page 294 of Leon.
For each of the matrices A in problem 1 above, determine if A is diagonalizable
(over the complex numbers).
For each of the matrices A of problem 1 whic
Matrix Theory HW 8. Not to be turned in.
1. Do the following problems from page 221 of Leon: 2; 3 for 3 b) nd a basis of the
orthogonal complement.
2. Use the algorithm of Lecture Note 8 to extend the set of linear independent vectors
cfw_(1, 2, 3, 5)T ,
Solutions to selected problems on HW 8.
Solution to Problem 3. Let
1
2
A=
1
3
2
3
.
1
5
Then W = column space(A) so
W = [column space(A)] = N (AT )
by formula (1) of Lecture Note 8.
AT =
1 2 1 3
2 3 1 5
has the RRE form
1 0 1 1
0 1 1 1
The standard fo
Matrix Theory HW 5. Not to turn in.
1. Use one of Algorithms 5 or 7 from Handout 5 on Algorithms to compute bases to
solve the following problems. Show your work, rst writing down an appropriate
matrix, to be transformed by elementary row operations.
a) F
Matrix Theory HW 4. Not to turn in.
Do the following problems from Leon.
page 125: 2, 5, 20, 21.
page 137: 2 (d), (e); 8 (a), (b), (c). If the given vectors are linearly dependent write
out a specic dependence relation; 16.
1
Matrix Theory 4140 HW 3. Not to turn in.
Do the following problems from Leon.
page 90: 3, 6.
page 97: 2,4,5,6,11,12.
page 105: 1 (why does (i) tell you that A is invertible?), 2 (a) and (c), 10, 11, 12.
i) Find the area of the parallelogram spanned by v1