Math 2700 Linear Algebra
SAMPLE TEST 1
February 2012
Instructor : William Cherry
Department of Mathematics
University of North Texas
I arm that I did not receive or give aid to others
while taking this test and that what is written in this
test represents
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Math 2700 Quiz 3
February 5, 2014
Solutions
1
0
1
0 , 1 and 0 linearly independent?
I. Are the vectors
1
2
2
SOLUTION: In order to show that the vectors are linearly independent, we must show
given
1
0
1
0 + x2 1 + x3 0 = 0 has only the trivial soluti
Math 2700 Quiz 2
January 29, 2014
Name:
5
21
I. Is 0 in the subset of R3 spanned by the columns of 1 2 .
7
31
1
II. Let u = 0 . Find a 23 matrix A, with no zero entries, such that Au = 0.
1
Math 2700, Quiz 2
January 29, 2014
Solutions
5
21
I. Is 0 in the subset of R3 spanned by the columns of 1 2 .
7
31
SOLUTION: The
2
1
vector equation x1 1 + x2 2 =
3
1
5
1
0 . This matrix is row equivalent to 0
7
0
5
0
7
2
1
0
has corresponding augmented
Math 2700 Quiz 1
January 22, 2014
Name:
I. Find the reduced echelon form of the following matrix.
1321
2 6 5 3
1322
II. Determine whether or not the vector
is a linear combination of the vectors
1
3
1
3
2
3
and
2
1
1
Math 2700 Quiz 1
January 22, 2014
Solutions
I. Find the reduced echelon form of the following matrix.
1321
2 6 5 3
1322
SOLUTION: Subtract the rst row from the
yields the matrix
1
0
0
third and twice the rst row from the second. This
321
0 1 1
001
Now sub
Math 2700
Midterm 1 solutions
11514
1. (10 points) Find the reduced row echelon form of the matrix 1 2 8 1 5 .
2 3 13 3 10
10202
SOLUTION: The reduced row echelon form of the given matrix is 0 1 3 0 1 .
00011
2. (a) (5 points) Complete the following denit
Math 2700
Concept review sheet for MT1
I. Give an example of a matrix that is in echelon form and not in reduced echelon form. Give an
example of a matrix that is in reduced echelon form.
II. Consider the function T : R3 R3 , given by
T (x1 , x2 , x3 ) =
Math 2700 Quiz 3
February 5, 2014
Name:
1
0
1
0 , 1 and 0 linearly independent?
I. Are the vectors
1
2
2
II. Find a 2 2 matrix A such that, for each vector x in R2 , the vector Ax has the same length
as x, but is rotated 90 counterclockwise.
Math 2700 Quiz 4
February 12, 2014
Solutions
1
0
1
2 , 1 and 0 span R3 ?
I. Do the vectors
1
3
1
101
SOLUTION: The matrix X = 2 1 0 is row equivalent to the 3 3 identity matrix. Thus
131
X is invertible. It follows that the columns of X span R3 .
II. F
Math 2700 - Review for Final Exam (December 2012).
SHOW ALL YOUR WORK! NO WORK=NO CREDIT!
1. Find the general solution of the following system of equations in parametric vector
form:
x1 +2x2 3x3 +x4 = 1
x1 x2 +4x3 x4 = 6
2x1 4x2 +7x3 x4 = 1
2. Find the in
Math 2700 - Review for Final Exam (April 2013)
SHOW ALL YOUR WORK! NO WORK=NO CREDIT!
1. Find the value of h such that the columns of
1 1 5
A= 0 3 h
2 4 6
are linearly dependent.
2. Find the general solution of the following system of equations in paramet
Math 2700 - Review for Exam 3 (April 2014)
P. Allaart
SHOW ALL YOUR WORK! NO WORK=NO CREDIT!
No Calculators Allowed! - But you shouldnt need any.
1. (11 pts.) Find the determinant of the matrix
1 0 5 3
3 0 2 4
1 2 1 4
1 0 2 0
You may use any method, but
Math 2700 - Review for Exam 1
P. Allaart
1. Describe all solutions of the equation Ax = 0 in parametric vector form, where A
is row-equivalent to the matrix
1 3 2 1 2 3
0 0 1 1 0 3
0 0 0 1 1 1
2. Let
1
1
3 , v2 = 1 ,
v1 =
3
1
1
h .
and b =
4
For whic
Math 2700 - Review for Exam 2
P. Allaart
SHOW ALL YOUR WORK! NO WORK=NO CREDIT!
No Calculators Allowed! - But you shouldnt need any.
1. Compute the following matrix products, if possible.
1 1 0
a) (7 pts.) AAT , where A = 1 1 1
0 1
1
b) (5 pts.)
1
3
2 1 5
Math 2700 Quiz 4
February 12, 2014
Name:
1
0
1
2 , 1 and 0 span R3 ?
I. Do the vectors
1
3
1
II. Find two nonzero 2 2 matrices A and B such that AB is the zero matrix.