Math 107 Third Midterm Examination November 22, 2005
NAME
(Please print)
Page Score 2 3 4 5 6 7 Total (Max Possible: 100)
Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Put answe
MATH 107.01
HOMEWORK #6 SOLUTIONS
Problem 1.6.4. Use Theorem 1.21 to determine if the matrix
2 1 3
3
A = 1 1
6 0
0
is invertible.
Solution. Compute
2
det (A) = 1
6
1
1
0
3
1
3 =6
1
0
3
= 6 (3 + 3) = 0.
3
Hence A is not invertible.
Problem 1.6.6. Use the a
MATH 107.01
HOMEWORK #10 SOLUTIONS
Problem 2.5.5. Show that x2 1, x2 + 1, x + 1 are linearly independent on R.
Solution. Note that
2
2
w x 1, x + 1, x + 1
x=0
x2 1
= 2x
2
x2 + 1
2x
2
x+1
1
0
2
x=0
1
= 0
2
1 1
0 1 = 4 = 0.
2 0
2
Theorem 2.15 in the book th
MATH 107.01
HOMEWORK #1 SOLUTIONS
Problem 1.1.2. Solve the system
2x + y 2z = 0
2x y 2z = 0
x + 2y 4z = 0
Solution. Note that
2
rref 2
1
1 2 0
1
1 2 0 = 0
2 4 0
0
0
1
0
0
0
1
0
0
0
Hence the only solution is
0
x
y = 0 .
0
z
Problem 1.1.8. Solve the sy
Math 107 Third Midterm Examination November 22, 2005
NAME
(Please print)
Page Score 2 3 4 5 6 7 8 9 10 Total (Max Possible: 100)
Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Pu
Math 107 Second Midterm Examination March 20, 2009
NAME
(Please print)
Page Score 2 3 4 5 6 7 8 Total
Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Put answers inside the boxes
Math 107 Second Midterm Examination October 24, 2008
NAME
(Please print)
Page Score 2 3 4 5 6 7 8 9 Total (Max Possible: 100)
Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Put a
MATH 107: EXAM 1
No calculators allowed. Your work must be clearly written in order to receive credit. Time: 50 minutes (1) (21 points) Let 2 1 -2 1 M = -1 3 -3 b = 1 4 -2 1 1 (a) (5 points) Compute the determinant of M by cofactor expansion alo
MATH 107: EXAM 2
No calculators allowed. Your work must be clearly written in order to receive credit. Time: 50 minutes (1) (10 pts) Let 3 0 0 A = -9 -1 5 -1 -1 3 (a) (9 pts) Compute the eigenvalues of A and a basis for each eigenspace. Clearly la
MATH 107: EXAM 3
No calculators allowed. Your work must be clearly written in order to receive credit. Time: 50 minutes (1) (15 pts) Find the general real-valued solution to the differential equation x + 2x + x = 4 sin 2t (2) (5 pts) Suppose that a
Ben Cooke
Math 107
Test 1
Do not open this test booklet until you are directed to do so. You have 50 minutes to earn 100 points. This exam is closed book. You are not allowed to use a calculator. Show your work, as partial credit will be given.
Ben Cooke
Math 107
Test 2
Do not open this test booklet until you are directed to do so. You have 50 minutes to earn 100 points. This exam is closed book. You are not allowed to use a calculator. Show your work, as partial credit will be given.
Ben Cooke
Math 107
Test 3
Do not open this test booklet until you are directed to do so. You have 50 minutes to earn 100 points. This exam is closed book. You are not allowed to use a calculator. Show your work, as partial credit will be given.
Ben Cooke
Math 107
Test 4
Do not open this test booklet until you are directed to do so. You have 50 minutes to earn 100 points. This exam is closed book. You are not allowed to use a calculator. Show your work, as partial credit will be given.
First Midterm February 19, 2009
NAME
(Please print)
Question Score 1 2 3 4 5 Total (Max Possible: 100)
Instructions: 1. All questions are worth 20 points. 2. No calculators, computers, notes, books are permitted. 3. Do all computations on the exa
Second Midterm February 19, 2009
NAME
(Please print)
Question Score 1 2 3 4 5 Total (Max Possible: 100)
Instructions: 1. All questions are worth 20 points. 2. No calculators, computers, notes, books are permitted. 3. Do all computations on the ex
Math 107 (06)
Exam 1
Spring 2009
Name:
Problem 1 (10pts). Complete the following definitions: (a) The vectors v1 , . . . , vk are linearly independent iff:
(b) W is a subspace of the vector space V iff:
(c) The n n matrix B is the inverse of
Math 107 (06)
Exam 2
Spring 2009
Name:
Problem 1. A tank initially contains 600 l of salted water whose salt concentration is 0.5 kg/l. Salted water whose salt concentration is 0.25 kg/l flows into the tank at the rate of 12 l/min. The mixture f