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Math 410 Take Home Exam 1 (Ch.1, 2.1)

Exam Instructions:

Use your own paper and hand write the solutions to each of the problems. You may use a tablet if you

wish. Put your name on each page . . just in case. Each problem should be completed on a its own sheet

or sheets of paper

When finished you will scan your exam solutions to PDF and submit it just like HW.

Show all work. Problems with an answer and no work will be give a zero, regardless of correctness.

You must show all your setup work. I want to see the integrals fully worked out by hand unless

otherwise stated in the problem.

You must work alone. No working in groups. No help from tutors or others. It must be your own

work.

If your work matches one or more person’s work, then ALL people with the matching work will

be given a 0 on that problem. Both the person copying and the person who allowed their work to

be copied will be penalized equally.

You may use the textbook, notes and anything from our class Canvas site.

You may use a graphing calculator except on problems that specifically ask that you solve by hand.

You may not make use of Wolfram Alpha, or any other online linear algebra resource to do your work

for you. If your work looks like it came from Wolfram Alpha, I’ll run the problem thru Wolfram myself.

If your work matches the output of Wolfram Alpha, the problem will be graded as a 0.

Exam is due at Mon, Oct5 @ 3:30pm sharp. The exam submission will close exactly at 3:30pm

and I will not accept late exams for any reason.

If you don’t get it in by 3:30pm, its a 0, no exceptions. You are being given an extremely liberal

5 day window to work on the exam. Plan to finish the exam by Mon, 9/28 @ Noon to give

yourself plenty of time to submit it. This way if anything goes wrong, or you have internet

problems, you can still contact me using your phone and we can work things out.

I will be available in office hours on Mon, 10/5 from 10:30 to Noon and via email from Noon

until 12:45p in the event you have a tech problem related to submission.

If you wait till the last minute to finish your exam and submit it and then miss the deadline, that’s

on you . . your fault and no one else’s. Seriously, plan to finish by Mon @ Noon so you have

time to deal with any problems. If you are finished earlier (Sat or Sun say) you are welcome to

turn it in earlier.

Check your file before you submit it! If pages are missing, those problems are a 0. If pages

are unreadable, those problems are a 0. Its your exam, your grade . . its your responsibility

to make sure the file is correct.

1. (6pts) Solve the following linear system of equations by hand. Show all your work.

2. (5pts) Use matrices to determine whether the following system of linear equations is consistent or

inconsistent and why. You may use a calculator but show your setup and results from your calculator.

3. For

C = [1 -1 -2]

Perform the following matrix operations by hand.

If an operation is not possible, write “Not possible” and explain why

a) (3pts)

b) (3pts)

c) (3pts)

4. (5pts) Solve the following system by hand and put your solution in parametric vector form

5. Given

vectors

and

a) (4pts) Is c a linear combination of

b) (4pts) Is c in span

c) (6pts) Do

? Show your work to justify your answer

? Why? Show your work to justify your answer

span all of

?

6. (6pts) Solve the matrix equation

for .

Write your answer as a column vector. You may use a calculator for this but show your problem setup and any

entries into your calculator as part of your work.

7. For

defined by

a) (4pts) Is b =

T( ) =

in Range(T)?

b) (4pts) Is T a linear transformation? Why or why not?

c) (4pts) Is T onto

? Show work to justify your answer

d) (4pts) Is T a 1-1 transformation? Show work to justify your answer

8. (7pts) Is

a linear transformation? Use the definition of linear

transformation to show why it is or is not

9. (7pts) The projection of vectors from

into

is a linear transformation defined by

.

Determine the standard matrix A for this transformation so that T(x) = Ax.

10. If

and

a) (2pts) Confirm that

is a solution to the non-homogeneous system Ax=b

b) (2pts) Confirm that

is a solution to the homogeneous system Ay=0

c) (3pts) Will any scalar multiple of y solve the homogeneous system Ay=0? Use properties of scalar

multiplication and matrix multiplication to show why or why not.

d) (3pts) Write the general solution to the non-homogeneous system Ax=b using parametric form

11. Determine by inspection whether the following sets of vectors are linearly dependent or linearly

independent and justify your answer by describing why

a) (3pts)

b) (3pts)

c) (3pts)

12. (6pts) Do the columns following matrix A form a linearly independent or linearly dependent set of vectors?

Justify your answer by showing all you work and showing any calculations you make or matrices you use to

come to that conclusion.

Purchase answer to see full

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Tags:

linear algebra

Matrix operations

system of equations

linear system

parametric vector

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