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Holt - Linear Algebra with Applications 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 25

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

Last Saved : n/a Saving...  ()

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Question
Points
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0/2 1/1 0/6 0/3 –/2 –/1 –/2 –/5 –/1 –/2
Total
1/25 (4.0%)

  • Instructions

    Linear Algebra with Applications, 2nd edition, written by Jeffrey Holt and published by W. H. Freeman, blends computational and conceptual topics throughout to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. The WebAssign component for this title engages students with immediate feedback on end-of-chapter questions, detailed solutions, a Personal Study Plan, and links to a complete eBook.

    Question 1 contains a linear system with infinitely many solutions, where any parameterization of the solution vector is accepted.

    Question 2 demonstrates grading for a list of equations that may be entered in any order, and each equation may be in any equivalent form.

    Question 3 is an example that preserves the pedagogy and the "explain" part of the question. The student determines whether or not a function is a linear transformation, and the answer blanks leave open the possibility for either case. The entries of the associated matrix may be entered using any equivalent value.

    Question 4 features expandable matrix answer blanks where the size of each matrix product is determined by the student, just as it would be on paper. Grading treats the entire matrix as a whole, and also handles non-existent matrices for impossible matrix operations.

    Question 5 exhibits an application of a linear transformation matrix to find the production level for three products that results in the specified costs.

    Question 6 utilizes the capability of the matrix grading to accept any stochastic matrix that meets the given criteria, but excludes the identity matrix.

    Question 7 showcases expandable vector answer blanks, where the student determines both the size and the number of vectors, while still being able to enter any equivalent basis.

    Question 8 illustrates how a characteristic polynomial can be entered in any form, eigenvalues can be listed in any order, and eigenvectors can incorporate any scalar multiple.

    Question 9 features differential equation grading that allows any arbitrary constants to be used for the general solution of the system.

    Question 10 handles the rounded coefficients of Fourier and discrete Fourier approximations in a single answer blank, while still allowing for a small tolerance. 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.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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

Your last submission is used for your score.

1. 0/2 points  |  Previous Answers HoltLinAlg2 1.2.023. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
2/100 1/100
Total
0/2
 
Convert the given system to an augmented matrix.
2x1 + 2x2 − x3 = 7
−x1 − x2 = −2
3x1 + 3x2 + x3 = 3
    

Find all solutions by reducing the system to echelon form and back substituting. (If there are an infinite number of solutions use
s1
 as your parameter. If there is no solution, enter NO SOLUTION.)
(x1, x2, x3) = 
NOdvs SOLUTION
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2. 1/1 points  |  Previous Answers HoltLinAlg2 2.1.008. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
Total
1/1
 
Express the given vector equation as a system of linear equations. (Enter your answers as a comma-separated list of equations.)
x1
−1
6
−3
 + x2
9
−5
0
 = 
−7
−10
2
−x1​+9x2​=−7,6x1​−5x2​=−10,−3x1​=2
Correct: Your answer is correct. webMathematica generated answer key

Solution or Explanation
−x1 + 9x2 = −7
6x1 − 5x2 = −10
−3x1 = 2
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3. 0/6 points  |  Previous Answers HoltLinAlg2 3.1.019. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
0/1 0/1 0/1 0/1 0/1 0/1
1/100 1/100 1/100 1/100 1/100 1/100
Total
0/6
 
Determine if the given function is a linear transformation.
T(x1, x2) = (x2 sin(π/4), x1 ln(3))
     Incorrect: Your answer is incorrect.

If so, identify the matrix A such that
T(x) = Ax.
 (If the function is not a linear transformation, enter DNE into all cells.)
A = 
DNE
Incorrect: Your answer is incorrect. webMathematica generated answer key
DNE
Incorrect: Your answer is incorrect. webMathematica generated answer key
DNE
Incorrect: Your answer is incorrect. webMathematica generated answer key
DNE
Incorrect: Your answer is incorrect. webMathematica generated answer key


If not, explain why not.
     Incorrect: Your answer is incorrect.


Solution or Explanation
Linear transformation, with
A =
0sin(π/4)
ln(3)0
.
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4. 0/3 points  |  Previous Answers HoltLinAlg2 3.2.004. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 –/1 –/1
1/100 0/100 0/100
Total
0/3
 
Perform the indicated computations when possible, using the matrices given below. (If an answer does not exist, enter DNE into any single cell.)
A = 
−31
2−1
,   B = 
03
−27
,    C = 
70
−13
33
,   E = 
13−7
−21−3
026
(a)    
A3


 Incorrect: Your answer is incorrect. seenKey

[-41,15; 30,-11]

(b)    
BCT

(c)    
EC + I3
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5. –/2 points HoltLinAlg2 3.3.071. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
A consumer electronics company makes two different types of smart phones, the
j8
 and the
j8+.
 Suppose that
j9
 corresponds to a new smart phone produced by the company. The manufacturing cost includes labor, materials, and overhead (facilities, etc.). The company's costs (in dollars) per unit for each type are summarized in the following table.
    
j8
 		    
j8+
 		    
j9
Labor 57 73 81
Materials 93 101 113
Overhead 29 34 38
Suppose T is the linear transformation that takes as input a vector of unit counts for
j8's, j8+'s, and j9's
 respectively, and produces for output a vector of total labor, material, and overhead, respectively. Find a formula for T. (A graphing calculator is recommended.)
T(x) =
x

Determine
T −1,
 and use it to find the production level for each type of phone that will result in the given costs.
Labor = $1598, Materials = $2306, Overhead = $762
(j8, j8+, j9) = 
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6. –/1 points HoltLinAlg2 3.5.027. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Find an example that meets the given specifications.
A 2 × 2 stochastic matrix A that has
2/3
1/3
 for a steady-state vector.
A =
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7. –/2 points HoltLinAlg2 4.2.010. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Use the solution method from this example to find a basis for the given subspace.
S = span
1
0
−1
1
, 
4
1
0
4
, 
0
1
4
0
, 
5
1
−1
5








Give the dimension of the basis.
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8. –/5 points HoltLinAlg2 6.1.025. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
Consider the matrix A.
A =
400
130
−45−1
Find the characteristic polynomial for the matrix A. (Write your answer in terms of λ.)


Find the real eigenvalues for the matrix A. (Enter your answers as a comma-separated list.)
λ =


Find a basis for each eigenspace for the matrix A.

    (smallest eigenvalue)


    (largest eigenvalue)
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9. –/1 points HoltLinAlg2 6.4.011. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Find the general solution for the system.
y'1 = y1 + 64y2
y'2 = y1 + y2
(y1(t), y2(t)) = 
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10. –/2 points HoltLinAlg2 10.3.042. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Suppose that
f(x) = x2 + 3.
 (A graphing calculator is recommended. Round your coefficients to four decimal places.)

Find
f3(x).

f3(x) =


Generate a list of values of f corresponding to
x = 
2π
50
 − π, 
4π
50
 − π, 
6π
50
 − π,   , π,
 and use these to find
g3(x).

g3(x) =
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