Vectors - Applied Linear Algebra - Exam, Exams of Linear Algebra

This is the Exam of Applied Linear Algebra which includes Inconsistent, Matrix, Parallelogram, Precise Description etc. Its key important points are: Vectors, Linearly Independent, Transformation, Nonzero Vectors, Linearly Independent, Linear Transformation, Columns, Never One to One, Chemical Equation, Balance

Typology: Exams

2012/2013

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Math 232, Fall 2007
Midterm 1
Oct. 5, 2007
Last Name:
First Name:
SFU ID:
1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.
2. No calculators are allowed.
3. This test is comprised of 6 pages (including cover page)
4. Once the test begins, please check that all pages are intact.
5. Do ALL questions.
6. Clearly explain your answer. No credit will be given for just writing down the
answer.
7. If the answer space provided is not sufficient, write your answer on the back
of the previous page. Clearly mark the question number.
8. Good luck.
Question Points Score
1 7
2 10
3 10
4 11
5 12
Total: 50
pf3
pf4
pf5

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Math 232, Fall 2007

Midterm 1

Oct. 5, 2007

Last Name:

First Name:

SFU ID:

1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.

2. No calculators are allowed.

3. This test is comprised of 6 pages (including cover page)

4. Once the test begins, please check that all pages are intact.

5. Do ALL questions.

6. Clearly explain your answer. No credit will be given for just writing down the

answer.

7. If the answer space provided is not sufficient, write your answer on the back

of the previous page. Clearly mark the question number.

8. Good luck.

Question Points Score

Total: 50

  1. (7 points) Show that the vectors  

are linearly independent. Show all work.

  1. (10 points) Balance the chemical equation

B 2 S 3 + H 2 O −→ H 3 BO 3 + H 2 S using the vector equation approach. Show all work.

  1. Let T : R^3 → R^4 be the linear transformation given by

T

x 1 x 2 x 3

x 1 + 2x 2 − x 3 3 x 2 + x 1 + 2x 3 x 3 + x 1 x 2 + x 3

(a) (3 points) Find the matrix of T. Show all work. (b) (4 points) Is T one-to-one? Justify your answer. (c) (4 points) is T onto? Justify your answer.