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Poole - Linear Algebra: A Modern Intro 5/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : – / 53

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
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–/2 –/1 –/2 –/1 –/35 –/4 –/3 –/3 –/2
Total
–/53 (0.0%)

  • Instructions

    David Poole's innovative Linear Algebra: A Modern Introduction, 5th edition, published by Cengage Learning, emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes numerous applications drawn from a variety of disciplines, which reinforce that linear algebra is a valuable tool for modeling real-life problems. A wide range of end-of-section exercises are available in WebAssign to provide students ample opportunity to practice linear algebra concepts and techniques. Every section of the book includes a set of learning objectives as a useful guide for students and instructors alike.

    WebAssign provides a wide range of exercises that enable you to:
    • Build Problem Solving Skills (#1-3: Read Its and Watch Its)
    • Develop Conceptual Understanding (#4-7: Master It Tutorials, Expanded Problems and Explorations)
    • Support the Learning Process Outside the Classroom (#8-9: Video Examples and Concept Videos)

    This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

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1. –/2 points PooleLinAlg5 2.3.016. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
  • This exercise will build problem-solving skills.
  • Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.
Describe the span of the given vectors geometrically and algebraically.
u = 
0
−1
1
,  v = 
1
0
−1
,  w = 
−1
1
0
(a)
geometrically
    
(b)
algebraically (Enter a mathematical equation.)
The general equation in terms of x, y, and z is
.
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2. –/1 points PooleLinAlg5 3.4.004. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
  • This exercise will build problem-solving skills.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.
Solve the system A x = b using the given LU factorization of A.
A = 
2−60
3−46
−132
 = 
100
 
3
2
10
− 
1
2
01
 × 
2−60
056
002
,    b = 
6
−3
−7
x =

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3. –/2 points PooleLinAlg5 3.5.021. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
  • This exercise will build problem-solving skills.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.
Find bases for row(A) and col(A) in the given matrix using AT.
A = 
10−1
113
row(A)    

col(A)    

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4. –/1 points PooleLinAlg5 3.1.004.MI. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
  • This exercise will develop conceptual understanding.
  • Master It tutorials are an optional student-help tool available within select questions for just-in-time support. Students can use the tutorial to guide them through the problem-solving process step-by-step using different numbers.
Let
B =
6−51
056
,    C =
23
15
46
.
Compute the indicated matrix. (If this is not possible, enter DNE in any single blank).
C − BT

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5. –/35 points PooleLinAlg5 4.3.006.MI.SA. My Notes
Question Part
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–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/35
 
  • This exercise will develop conceptual understanding.
  • Master It tutorial - Standalone (.MI.SA) is a step-by-step tutorial-style exercise used to help and gauge students’ understanding of each step with required input on each step needed to solve the problem in addition to the final answer.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
Consider the following.
A = 
102
3−13
201
(a)
Compute the characteristic polynomial of A.
(b)
Compute the eigenvalues and bases of the corresponding eigenspaces of A.
(c)
Compute the algebraic and geometric multiplicity of each eigenvalue.

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6. –/4 points PooleLinAlg5 1.3.043.EP. My Notes
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–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
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–/4
 
  • This exercise will develop conceptual understanding.
  • Expanded Problems (.EP) enhance student understanding go beyond a basic exercise by asking students to show steps for their work or reasoning before reaching the final answer.
Consider the following planes.
2x + 2y + 2z = 0
 and
3x + y − 3z = 0
Find the normal vector to
2x + 2y + 2z = 0.
n1=
Find the normal vector to
3x + y − 3z = 0.
n2=
Find cos(θ), where θ is the angle between n1 and n2.
cos(θ) =
Find the acute angle (in degrees) between the planes with the given equations. (Round your answer to one decimal place.)
θ = °
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7. –/3 points PooleLinAlg5 4.2.Exp.012. My Notes
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–/3
 
  • This exercise will develop conceptual understanding.
  • Explorations (Exp) provide deeper discovery-based guides on key concepts, designed for individual or group work.
Prove that the three points
(x1, y1), (x2, y2), and (x3, y3)
 are collinear (lie on the same line) if and only if
x1  y1  1
x2  y2  1
x3  y3  1
 = 0.
Only three statements in the following scrambled list belong in the proof.
  • Statement 1: Which can be written as the matrix equation
    XA =  
    		x1y11
    x2y21
    x3y31
     
    		a
    b
    c
     = O.
  • Statement 2: Then, A ≠ O if and only if det(X) = 0; this says precisely that the three points lie on the line
    ax + by + c = 0
     with a and b not both zero if and only if det(X) = 0.
  • Statement 3: Consider the case when X is invertible which is true if and only if det(X) ≠ 0, which implies that
    X−1XA = X−1O = O,
     so that A = O.
  • Statement 4: Then, A = O if and only if det(X) ≠ 0; this says precisely that the three points do not lie on the line
    ax + by + c = 0
     with a and b not both zero if and only if det(X) ≠ 0.
  • Statement 5: Which can be written as the matrix equation
    XA =  
    		a
    b
    c
     
    		x1y11
    x2y21
    x3y31
     = O.
Construct the proof by choosing the appropriate statements from the list and putting them in the correct order.
  1. Suppose the three points satisfy
     
        ax1 + by1 + c = 0
    ax2 + by2 + c = 0
    ax3 + by3 + c = 0,
     
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8. –/3 points PooleLinAlg5 1.1.VE.002. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
  • This exercise will support learning outside the classroom.
  • Video Examples (VE) questions ask students to watch a section level video segment on key examples problems and then answer a question related to that video. Consider assigning the video questions as a review prior to class or as a lesson review prior to a quiz or test.

Vectors and Scalars

What are the vectors represented by the sides and diagonals of the parallelogram formed by two vectors
a and b?
Two vectors and four dashed lines are given. Two vectors begin at the same initial point, one labeled
a
 and the other labeled
b.
 The first dashed line labeled
p
 begins where
a
 ends, runs parallel to
b,
 and is the same length as
b.
 The second dashed line labeled
r
 begins where
b
 ends, runs parallel to
a
 and is the same length as
a.
p
 and
r
 meet at a point. The third dashed line labeled
q
 begins at the same initial point as
a
 and
b
 and ends at the point where
p
 and
r
 meet. The fourth dashed line is unlabeled, it connects the ending points of
a
 and
b.
What vector does
p
 represent?
    
What vector does
q
 represent?
    
What vector does
 r
 represent?
    
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9. –/2 points PooleLinAlg5 2.3.CV.001. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
  • This exercise will support learning outside the classroom.
  • Concept Video (CV) questions ask students to watch a section level video segment focusing on conceptual understanding and then answer a question related to that video. Consider assigning the video questions as a review prior to class or as a lesson review prior to a quiz or test.

Linear Combinations, Span, and Basis Vectors

What are all of the possible spans for a pair of vectors in two-dimensional space? (Select all that apply.)

What are all of the possible spans for a set of three vectors in three-dimension space? (Select all that apply.)

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