Math 331 practice problems for material covered after Midterm 2 Solutions
This is a list of practice problems for Math 331-Wylie covering material after the second midterm.
1. True of False:
(a) If A is a 4 4 matrix with two eigenvalues and one eigenspace
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Math 331 - Quiz 9 - Solutions
Thursday, November 17
1. Let
30
21
A=
Find a basis of the eigenspace corresponding to the eigenvalue = 3.
Solution:
A 3I =
00
.
2 2
0 0 |0
2 2 | 0
1 1 | 0
0 0 |0
So we have x2 is a free variable and
Nul(A 3I ) =
So a b
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Math 331 - Quiz 7 - Solutions
Thursday, October 27
1. Find an LU -factorization of
2
5
3 4
Solution: Row reduce the matrix to echelon form.
2
5
3 4
Then U =
25
7
02
and L =
1
3
2
II+ 3 I
25
07
2
2
0
.
1
Check:
LU =
2. Let
The echelon form of A is
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Math 331 - Quiz 5 - Solutions
Thursday, October 13
3 6
. Construct a 2 2 matrix B which has two dierent nonzero columns
2 4
such that AB is the zero matrix.
1. Let A =
Solution:
Write B in terms of its columns
B=
b1 b2
Then
AB =
Ab1 Ab2
So if AB =
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Math 331 - Quiz 4 - Solutions
Thursday, October 6
1. Assume that T is a linear transformation. Find the standard matrix of T if T : R2 R4 ,
T (e1 ) = (3, 1, 3, 1) and T (e2 ) = (5, 2, 0, 0) where e1 = (1, 0) and e2 = (0, 1).
Solution: The standard
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Math 331 - Quiz 3 - Solutions
Thursday, September 22
1. Describe all of the solutions to Ax = 0 in parametric form
1 4 2
0 0
1
A=
0 0
0
00
0
0
0
0
0
3 5
0 1
1 4
00
The free variables are x2 , x4 ,and x6 . The matrix is in echelon form but not red
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Math 331 - Quiz 2
Thursday, September 15
1. Construct a 3 3 matrix A with nonzero entries and a vector b in R3 such that b is not in
the set spanned by the columns of A. Justify your answer.
Solution:
There are many possible answers to this questio
Math 331 - Quiz 1 - Solutions
Thursday, September 8
1. Determine whether the following matrices are in echelon form, reduced row echelon form, or
neither. Justify your answer.
1000
(a) 0 2 0 0
0011
Solution:
in reduced
000
1 2 0
(b)
0 0 1
000
The matrix
Math 331 - Orthogonal Projections Worksheet
Here are some Practice problems on nding the standard matrix of an orthogonal projection,
1. Let L be the line thru the origin in R2 that is parallel to the vector
3
.
4
(a) Find the standard matrix of the ortho
Math 331 - Orthogonal Projections Worksheet - Solutions
Here are some Practice problems on nding the standard matrix of an orthogonal projection,
1. Let L be the line thru the origin in R2 that is parallel to the vector
3
.
4
(a) Find the standard matrix
.
Math 331 Wylie Midterm 2 Solutions November 3, 2011
1. True of False:
(a) If A and B are invertible n n matrices then AB = BA.
False
(b) If an n n matrix A has linearly independent columns and the columns of another n n
matrix B span Rn , then the colum
Math 331 Midterm 2 practice problems
This is a list of practice problems for the rst midterm in Math 331 (Wylie). The actual exam
will be 10 problems long with each problem worth 10 points. The rst problem on the exam will
be similar to the rst practice p
Math 331 Midterm 2 practice problems
This is a list of practice problems for the rst midterm in Math 331 (Wylie). The actual exam
will be 10 problems long with each problem worth 10 points. The rst problem on the exam will
be similar to the rst practice p
.
Name: .
Math 331 Wylie Midterm 1 September 27, 2011
This is the rst midterm exam in Math 331. There are ten questions and each question is worth
10 points. No notes are allowed. You are allowed only a standard scientic calculator (although the
exam has
.
Name: .
Math 331 Wylie Midterm 1 September 27, 2011
This is the rst midterm exam in Math 331. There are ten questions and each question is worth
10 points. No notes are allowed. You are allowed only a standard scientic calculator (although the
exam has
Math 331 Midterm 1 practice problems
This is a list of practice problems for the rst midterm in Math 331 (Wylie). The actual exam
will be 10 problems long with each problem worth 10 points. The rst problem on the exam will
be similar to the rst practice p
Math 331 Midterm 1 practice problems
This is a list of practice problems for the rst midterm in Math 331 (Wylie). The actual exam
will be 10 problems long with each problem worth 10 points. The rst problem on the exam will
be similar to the rst practice p
Math 331-M001-Syllabus
Instructor: Dr. William Wylie, Assistant Professor of Mathematics
email: wwylie@syr.edu
Oce: 317H Carnegie
Phone: 3-1578
Oce Hours: T 11-12:30, W 1-2:30, or by appointment.
Course Supervisor: Dr. Gregory Verchota, Professor of Mathe
Name:.
Math 331 - Quiz 11
Thursday, December 8
1. Let
A=
05
2 2
nd an invertible matrix P and a rotation plus scaling matrix of the form
C=
a b
ba
such that A = P CP 1 .
Solution:
First we nd the characteristic polynomial
det (A I ) = det
5
2 2
= ()(2 )