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answer. Answers with no justication will not be graded.
Question 1: Let A = [c1 . . . c
Math 601 Midterm 1 Sample
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This exam has 9 questions, for a total of 100 points.
Please answer each question in the space provided. You need to write full solutions.
Answers without justication will not be graded. Cross out anything the grader should
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Mid term exam 1 (Notes, books, and calculators are not authorized)
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Question 1: Find a par
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Mid term exam 1 (Notes, books, and calculators are not authorized)
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Question 1: Find the e
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Mid term exam 1 (Notes, books, and calculators are not authorized)
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Question 1: Find a par
Math 601 Midterm 1
Name:
This exam has 9 questions, for a total of 100 points.
Please answer each question in the space provided. You need to write full solutions.
Answers without justication will not be graded. Cross out anything the grader should
ignore
Spring 2014
Math 601
Name:
Quiz 1 sample
Question 1. (12 pts)
(a) (5 pts) Find equations of the line L that passes through the points A(1, 0, 4, 3) and
B(3, 2, 0, 1).
Solution: First, calculate the direction of the line:
#
AB = (2, 2, 4, 2)
Then the equa
10.
Section 2 61
(c) The reduced row echelon form of A is
1 0
0 1
0 0
0 0
N(A) = {(0, 0)T} and {(1, 0)T, (0, 1)T} is a basis for R(AT). The
reduced row echelon form of AT is
55
10mm
411
0177
We can obtain a basis for R(A) by transposing the rows of U and
Spring 2014
Math 601
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Quiz 1
Question 1. (12 pts)
(a) (6 pts) Find equations of the line L that passes through the point A(1, 0, 4, 3) and
is perpendicular to the plane x1 + x2 + x3 + x4 = 1.
Solution: The direction of the line is
(1, 1, 1, 1)
the eq
Spring 2014
Math 601
Name:
Quiz 2
Question 1. (10 pts)
Solve the following linear system
2x + 8y + 4z = 2
2x + 5y + z = 5
4x + 10y z = 1
Solution: Set up the augmented coecient matrix
2 8 4 2
2 5 1 5
4 10 1 1
change it to its echelon form
1 4 2 1
0 1 1 1
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3 5 6
Question 1: Compute the L
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a 4
1
X=
.
2 a
b
(a) For which
Spring 2014
Math 601
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Quiz 4
Question 1. (8 pts)
Determine whether the following statements are true or false. If false, explain why.
(a) V is a vector space of dimension n and S is a set of vectors in V . If S spans V ,
then the number of vectors in
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Question 1: Let A =
1
1
0 1
1
Spring 2014
Math 601
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Quiz 4 sample
Question 1. (10 pts)
Determine whether the following statements are true or false. If false, explain why.
(a) If a vector space V has dimension n, then any n + 1 vectors in V must span V .
Solution: False. For exam
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Question 1: Find a parametric r
Spring 2014
Math 601
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Quiz 3
Question 1. (12 pts)
Determine if the given subset is a subspace of the corresponding vector space. (Show
work!).
(a) (4 pts) The subset of R3 :
W = cfw_v R3 | v (1, 2, 3) = 0
Solution: Yes, W is a subspace. I leave it to
Spring 2014
Math 601
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Quiz 3 sample
Question 1. (10 pts)
Determine if the given subset is a subspace of the corresponding vector space. (Show
work!).
(a) (5 pts) The subset of R3 :
W = cfw_(x, y, z) R3 | x + y + z 0
Solution: Consider u = (1, 1, 1).
Section 1 51
11. If L is a linear operator from V into W use mathematical induction to prove
L(a1v1 + a2v2 + - - + anvn) = a1L(v1) + a2L(vQ) + - - - + anL(vn).
Proof: In the case n = 1
L(01V1) = alL(Vl)
Let us assume the result is true for any linear com
SEVENTH EDITION
LINEAR
ALGEBRA WITH
APPLICATIONS
Instructors Solutions Manual
Steven J. Leon
PREFACE
This solutions manual is designed to accompany the seventh edition of Linear
Algebra with Applications by Steven J. Leon. The answers in this manual suppl