Math 330
Exam Reviews
Click on the links below for
sets of review problems and other review materials.
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Exam 1: (sections 1.1 to 2.2)
Exam 2: (sections 2.3 to 4.4)
-
Review Problems with
solutions
- Study the "True/False" and "Explain..." questions from the homework!
- Be able to give definitions for the following terms:
- linear transformation from V to W (4.2)
- nulA and colA (4.2)
- kernel and range of a linear transformation (4.2)
- linearly independent set of vectors in a vector space (4.3)
- basis for a vector space (4.4)
- Also, I may ask you to prove one of the following things:
- (j) implies (d) from the IMT
- (d) implies (c) from the IMT
- A is invertible if and only if
detA is not zero. (See Theorem 4 on p.194.)
- If A is an m by n matrix then nulA is a subspace
of Rn. (See Theorem 2 on p.227.)
- Exam
from previous semester with
answers
Exam 3: (sections 4.5 to 6.4)
-
Exam 3 Review Problems with
solutions
- Study the "True/False" and "Explain..." questions from the homework!
- Be able to give definitions for the following terms:
- dimension of a vector space
- rank of a matrix
- row space of a matrix
- eigenvector, eigenvalue, and eigenspace
- similar matrices (5.2)
- orthogonal set, orthonormal set (6.2)
- orthogonal matrix (6.2)
- Also, I may ask you to prove one of the following things:
- If there is a basis for Rn consisting of eigenvectors
for a matrix A then A = PDP-1 where P is the matrix with
columns equal to the basis of eigenvectors and D is a diagonal matrix
with the corresponding eigenvalues on the diagonal.
(Half of Theorem 5 on p.320.)
- Every orthogonal set of nonzero vectors is linearly independent.
(Theorem 4 on p.384.)
- Exam
from previous semester with
answers