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Muncaster - Applied Linear Algebra 1/e (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
0/1 1/1 0/1 –/12 2/2 0/3 –/1 –/3
Total
3/24 (12.5%)

  • Instructions

    The Applied Linear Algebra question collection contains more than 170 original questions with randomized answers that correspond to any introduction to linear algebra textbook. This collection was created by Bob Muncaster, an associate professor of mathematics at the University of Illinois at Urbana-Champaign and a longtime WebAssign user. Additional resources will be available soon.

    Question 2 asks for a comma-separated list of equations that forms the equivalent linear system of equations.

    Question 3 uses the matrix tool, which lets student define the size of the resulting matrix.

    Question 4 is a stepped problem that guides the student through the key steps to applying Gauss-Jordan elimination.

    Question 5 uses the matrix tool and grading that allows any correct row echelon form to be accepted. Try different correct answers.

    Question 6 showcases grading for bases, which accepts any correct column space or null space.

    Question 7 uses differential equation grading to test the validity of the answer. It accepts any correct form of the answer and runs student's responses through a series of tests to ensure the assumptions and requirements of the question are met.

    View the complete list of WebAssign questions available for this textbook. 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 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. 0/1 points  |  Previous Answers MuncasterLinAlg1 1.2.003. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Solve for x and z. (If an answer does not exist, enter DNE.)
−2
3
x
−4
 + 7
−3
4
z
 =
−27
3
−4
(x, z) = 
12.5, 127​
Incorrect: Your answer is incorrect. webMathematica generated answer key
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2. 1/1 points  |  Previous Answers MuncasterLinAlg1 1.2.005. My Notes
Question Part
Points
Submissions Used
1
1/1
1/50
Total
1/1
 
For the linear combination problem below find the equivalent linear system of equations. (Enter your answers as a comma-separated list of three equations.)
x
5
−1
−6
  + y
−2
−7
3
  = 
11
−17
−12
5x−2y=11, −x−7y=−17, −6x+3y=−12
Correct: Your answer is correct. webMathematica generated answer key
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3. 0/1 points  |  Previous Answers MuncasterLinAlg1 1.4.008. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find the product.
A =
32−31
, B =
4
−4
−2
−1
AB =



Incorrect: Your answer is incorrect. seenKey

[9]
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4. –/12 points MuncasterLinAlg1 1.6.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12
–/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
Total
–/12
 
Given a linear system
Ax = b,
 if Gauss-Jordan elimination is applied to the augmented matrix
[A | b]
 the end result will be the augmented matrix
[I | A−1b] = [I | x]
 where x is the solution of the system (assuming A is invertible). For the following matrices, A and b, use Gauss-Jordan elimination (with no row exchanges) to find the solution of
Ax = b.
A =
20−3
−6−111
−2−16
 and b =
3
4
−1
[A | b]
 		=
20−3 3
−6−111 4
−2−16 −1
=
2
0
00
=
100
010
001

Therefore x is the following.
x =
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5. 2/2 points  |  Previous Answers MuncasterLinAlg1 2.2.001. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 2/50
Total
2/2
 
For the following matrix, find the row echelon form and the reduced row echelon form.
A =
2922
63072
(a) row echelon form
Correct: Your answer is correct. seenKey

[2, 9, 22; 0, 3, 6]

(b) reduced row echelon form
Correct: Your answer is correct. seenKey

[1,0,2;0,1,2]
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6. 0/3 points  |  Previous Answers MuncasterLinAlg1 2.3.001. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 0/1 –/1
1/50 1/50 0/50
Total
0/3
 
For the given matrix, find the following.
A =
1113
2238
(a) Find the reduced row echelon form of A.
Incorrect: Your answer is incorrect. seenKey

[1, 1, 0, 1; 0, 0, 1, 2]

(b) Find a basis of the column space C(A) expressed in terms of columns of A.




Incorrect: Your answer is incorrect. seenKey

[1,1;2,3]





(c) Find a basis of the null space N(A).







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7. –/1 points MuncasterLinAlg1 5.1.001. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find the general solution of the linear system of differential equations where c1 and c2 are arbitrary real numbers. (Enter each vector in the form [x1, x2, ...].)
 
du
dt
 =
144
−24−6
u
u(t) =
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8. –/3 points MuncasterLinAlg1 6.1.002. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Given matrix A, determine the following.
A =
39−6
928−20
−6−2020
(a) Which of the following is an equivalent row echelon form?
    

(b) Using part (a), find the pivots of the matrix A. (Enter your answers as a comma-separated list.)


(c) Is the matrix positive definite?
    
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