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Holt - Linear Algebra with Applications 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 2 / 18

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

Last Saved : n/a Saving...  ()

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2/18 (11.1%)

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    W. H. Freeman and WebAssign



    W. H. Freeman and WebAssign have partnered to deliver an outstanding resource for your Linear Algebra course. Jeffrey Holt's Linear Algebra with Applications is rigorous without being inaccessible and clear without being too informal-it has the perfect balance for instructors and their students.

    WebAssign Premium for Holt's Linear Algebra will have approximately 1100 questions with solutions available to students by instructor choice. In addition to these questions, it offers a fully searchable eBook linked to questions and algorithmic solutions. Click here to learn more about the distinct features of this text.

    Below are some textbook questions from Linear Algebra with Applications 1/e by Jeffrey Holt published by W. H. Freeman. Questions 1 and 4 are examples of expandable matrix questions. To expand the matrix, click on any outward facing arrow or to contract the matrix, click on any inward facing arrow.

    Click here for a list of all of the questions coded in WebAssign. 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.

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1. –/2 points HoltLinAlg1 3.1.001. My Notes
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–/2
 
Let
T(x) = Ax
 for the given matrix A, and find
T(u1) and T(u2)
 for the given u1 and u2.
A =
32
−45
,    u1 =
−4
−3
,    u2 =
2
−5
T(u1) =

T(u2) =

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2. 1/6 points  |  Previous Answers HoltLinAlg1 3.1.019. My Notes
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1 2 3 4 5 6
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1/6
 
Determine if the given function is a linear transformation.
T(x1, x2) = (x2 sin(π/3), x1 ln(4))
     Correct: Your answer is correct.

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 = 


If not, explain why not.
     Incorrect: Your answer is incorrect.
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3. 0/1 points  |  Previous Answers HoltLinAlg1 3.1.031. My Notes
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1
0/1
1/50
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0/1
 
Suppose that
T(x) = Ax
 for the given A. Sketch a graph of the image under T of the unit square in the first quadrant of R2.
A =
1−6
71

Incorrect: Your answer is incorrect.


Solution or Explanation
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4. 0/3 points  |  Previous Answers HoltLinAlg1 3.2.004. My Notes
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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

(b)    
BCT


 Incorrect: Your answer is incorrect. seenKey

[0, 9, 9; -14, 23, 15]

(c)    
EC + I3
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5. –/1 points HoltLinAlg1 3.3.018. My Notes
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–/1
 
Use the inverse of
12−1
−4−77
−1−15
 to find the solutions to the linear system below.
x1 + 2x2 − x3 = −3
−4x1 − 7x2 + 7x3 = 2
−x1 − x2 + 5x3 = −2
(x1, x2, x3) = 
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6. 1/2 points  |  Previous Answers HoltLinAlg1 3.3.071. My Notes
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1/2
 
A consumer electronics company makes three different types of MP3 players, the J8 (8 GB), the J40 (40 GB), and the J80 (80 GB). 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     J40     J80
Labor 15 46 65
Materials 14 43 61
Overhead 20 60 81
The linear transformation
T(x)
 defined below gives the costs associated with a production vector x.
T(x) = 
154665
144361
206081
x1
x2
x3
Determine
T−1,
 and use it to find the production level for each type of player that will result in the given costs.
Labor = $2498, Materials = $2340, and Overhead = $3182.
(J8, J40, J80) = 


If the given costs are not possible, explain why.
     Correct: Your answer is correct.
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7. –/3 points HoltLinAlg1 3.5.046. My Notes
Question Part
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–/3
 
In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 95% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 760 employees at work. (A graphing calculator is recommended.)
(a) Find the transition matrix A for this scenario.
           at work        absent    
A =

(b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.)
employees

(c) Find the steady-state vector x. (Round your answer to two decimal places.)
x =
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