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Larson - Elementary Linear Algebra 8/e (Metric) (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 3 / 24

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

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9
3/3 0/2 0/1 –/3 –/1 –/8 0/1 –/1 –/4
Total
3/24 (12.5%)

  • Instructions

    Elementary Linear Algebra (Metric Version), 8th edition, by Ron Larson and published by Cengage Learning, provides a clear, careful, and concise presentation of material, written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Data and applications reflect current statistics and examples to engage students and demonstrate the link between theory and practice. This title is supported by WebAssign with an eBook, instant student feedback, and a Course Pack of premade assignments. The companion website LarsonLinearAlgebra.com also offers free access to multiple tools and resources to supplement students' learning.

    Question 1 handles any ordered list for a set of constants that satisfy certain conditions, as well as an impossible answer.

    Question 2 demonstrates expandable matrix answer blanks that grade the matrix as a whole, and also handles answers for matrices that cannot be computed.

    Question 3 shows grading for a randomized list of values that can be entered in any order.

    Question 4 is a Step-by-Step question that walks the student through finding a determinant by asking for intermediate values.

    Question 5 features grading that accepts any equivalent equation for the plane.

    Question 6 is a multi-part question that has the student write the general solution of a differential equation using arbitrary constants.

    Question 7 contains a Master It tutorial that guides the student through a similar problem, encouraging them to work through each step by checking intermediate values. It also uses vector grading that allows the negative unit orthogonal vector to be entered.

    Question 8 utilizes grading for the general antiderivative of a function, enforcing proper use of + C and absolute values.

    Question 9 is a multi-part question finding the eigenvalues and eigenvectors of a randomized matrix, where any scalar multiple of the vectors are accepted as correct. 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. 3/3 points  |  Previous Answers LarLinAlg8M 1.2.051. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 2/100 1/100
Total
3/3
 
Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
x + y = 8
y + z = 8
x + z = 8
ax + by + cz = 0
(a) a unique solution
(a, b, c) = 
0,0,0
Correct: Your answer is correct. webMathematica generated answer key


(b) no solution
(a, b, c) = 
1,2,3


(c) infinitely many solutions
(a, b, c) = 
impossible
Correct: Your answer is correct. IMPOSSIBLE
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2. 0/2 points  |  Previous Answers LarLinAlg8M 2.1.019. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
1/100 1/100
Total
0/2
 
Find, if possible, AB and BA. (If not possible, enter IMPOSSIBLE in any single cell.)
A =
21
−43
16
,     B =
0−10
302
8−17
(a)    AB

 Incorrect: Your answer is incorrect. seenKey

IMPOSSIBLE
(b)    BA

 Incorrect: Your answer is incorrect. seenKey

[4,-3; 8, 15; 27, 47]
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3. 0/1 points  |  Previous Answers LarLinAlg8M 3.1.051. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
Find the values of λ for which the determinant is zero. (Enter your answers as a comma-separated list.)
λ  4    0
0  λ + 3    2
0  2    λ
λ =
[π 4 9]
Incorrect: Your answer is incorrect. webMathematica generated answer key
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4. –/3 points LarLinAlg8M 3.2.022.SBS. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
Use either elementary row or column operations, or cofactor expansion, to find the determinant by hand. Then use a software program or a graphing utility to verify your answer.
1  5  1
0  2  0
5  1  2
STEP 1: Expand by cofactors along the second row.

1  5  1
0  2  0
5  1  2
 = 2

STEP 2: Find the determinant of the 2x2 matrix found in Step 1.
STEP 3: Find the determinant of the original matrix.
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5. –/1 points LarLinAlg8M 3.4.056. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Find an equation of the plane passing through the given points.
(3, −2, 9), (4, 1, 5), (2, 2, 6)
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6. –/8 points LarLinAlg8M 4.8.031. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/8
 
Consider the following.
Differential Equation Solutions
y'' + 16y = 0
{sin 4x, cos 4x}
(a) Verify that each solution satisfies the differential equation.
y = sin 4x
y' = 
y'' = 
y'' + 16y = 


y = cos 4x
y' = 
y'' = 
y'' + 16y = 


(b) Test the set of solutions for linear independence.
    

(c) If the set is linearly independent, then write the general solution of the differential equation. (If the system is dependent, enter DEPENDENT. Use C1 and C2 for any needed constants.)
y =
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7. 0/1 points  |  Previous Answers LarLinAlg8M 5.5.038.MI. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
Find a unit vector orthogonal to both u and v.
u = i + 2j
v = i − 3k
5,5
Incorrect: Your answer is incorrect. webMathematica generated answer key

Solution or Explanation
u × v = 
i    j    k
1    2    0
1    0    −3
 = −6i + 3j − 2k
u × v
 = 
36 + 9 + 4
 = 7
unit vector = 
u × v
u × v
 = − 
6
7
i + 
3
7
j − 
2
7
k

Need Help? Master It

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8. –/1 points LarLinAlg8M 6.1.064. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Let
Dx
 be the linear transformation from
C' [a, b] into C[a, b].
 Find the preimage of the function. (Use C for the constant of integration. Remember to use absolute values where appropriate.)
Dx(f) = 
3
x
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9. –/4 points LarLinAlg8M 7.1.015. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
Total
–/4
 
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix.
8−4
−21
(a) the characteristic equation


(b) the eigenvalues (Enter your answers from smallest to largest.)
(λ1, λ2) = 


the corresponding eigenvectors
x1 = 
x2 = 
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