Office: 216 Love (enter through 208 Love)
Office hours: W 1:30--3:30pm
Phone: 664-8704
Email: agashe@math.fsu.edu
The final will be held on Tuesday April 22, 10am--12 noon.
It will be based on sections 2.9, 5.1, 5.2., 5.3, 5.4, 6.1, 6.2, 6.3, and
6.4
(in section 6.4, skip the portion in the book called "QR factorization
of matrices")
You are allowed to bring one 8.5 inches x 11 inches sheet of paper with anything written on both sides.
Calculators will not be allowed (the problems will be such that you won't need a calculator).
Note: There is a mistake in the answer to the very first problem in the sample final.
A correct answer for a basis for the column space of A is the 1st, 2nd, and 4th columns of A.
Answers to some true/false questions:
Section 1.8:
21 a. True, b. False, c. False:
d. Skip (the question is a bit advanced), e. True
Section 1.9:
23: a. True, b. True, c. False: it always is.
d. False, e. False: it can be one-to-one.
Section 2.2:
9: a. True, b. False, c. False,
d. True, e. True.
Section 2.3:
11: a. True, b. True, c. False: take A to be any non-invertible matrix,
for example, the zero matrix,
d. True, e. True. (all follow by the invertible matrix theorem).
Section 2.8:
21. a. Skip (the question is too ambiguous), b. True, c. False, d. True,
e. True.
Section 2.9:
17. a. True, b. False: the line must pass through the origin to be a subspace, c. True, d. True, e. True.
Section 5.1:
21. a. False: x could be the zero vector, b. True, c. True,
d. True, e. False.
Section 5.2:
21. a. False: it works only for triangular matrices,
b. False: for example, scaling changes the determinant,
c. True, d. False: -5 is an eigenvalue, not 5.
Section 5.3:
21. a. False: D must be diagonal, b. True, c. False,
d. False: for example, the zero matrix.
22: a. False: the eigenvectors may be linearly dependent,
b. False, c. True, d. False.
24: No, by Theorem 7(b).
Section 6.1:
19. a. True, b. True, c. True (see the discussion of Figure 5 in the book), d. False
e. True.
Section 6.2:
23. a. True, b. True, c. False, d. False: the matrix must also be square,
e. False.
Section 6.3:
21. a. True, b. True, c. False, d. True, e. True.