代写math – math207, Section 5

2023-07-07

math207, Section 5

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 math 207, Section 5 ( online)
Spring 2022
Exam 1
Time Limit: 1 hour 35 minutes

Name: _________ _
Section: _________ _
Instructor: _________ _

This exam contains 6 pages (including this cover page) and 5 questions. There are 100 points total. Show all of your work for full credit.

Grade Table (for teacher use only)
Question Points Score
1 20

2 20

3 20
4 20

5 20
Total: 100

. -.

  1. (20 points) For each system of equations below, use the row reduction algorithm and find the solution set (if any) in parametric vector form.

(a) (10 points) Ax= b, with

A = -1 1 2 -1 b= –

[
o 1 1 -

######## l [

5

######## l

(b)(10 points) Ax= 0, with

0 1 1 0^5

[

(^3) – 1 1

######## l

A= 0^3 1 4
0

3

-I I
( ti

I

Bookwalter

Fog

-8*-

@h@-g

  1. (20 points)
(a) (6 points) Label each matrix as Row Echelon Form (REF), Reduced Row Echelon
Form (RREF), or neither, and explain why:

(b) (8 points) Consider a system Ax= b. Suppose its augmented matrix [Ab] is row
equivalent to

[

' =~ l 
,0 0 0 0
Find the solution set in parametric vector form.
(c) (3 points) In part (b), is the vector bin the span of the columns of A? Justify your
answer. I
(d) (3 points) In ~art (b), for this particular choice of vector b, how many solutions
-. does the equation Ax= b have? Justify your answer.
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)(
3

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~-.

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####### –

  1. (_20 poin~s) For what value(s) of the parameter hare the three vectors {v 1 , v 2 , v 3 } below linearly mdependent?

–

_zzBotM

Bathyal

BaoqBE@Bm@rq

4. (20 points) Let T: JR3 JR4 be th e li near trans f ormat1on given by

T ( [ :: l ) = [ ::

1
; 3X:2-=- 2;;3 l 
X3 2x2 - X
6x1 - 2x 2 - 4x 3

(a) (6 points) Find the standard matrix for T.
(b) ( 7 points) Is T one-to-one?  Just1 f Y your answer.
(c) (7 points) Is Tonto?  Justl'fy Y 0 ur answer.

7D
_EA--__BzBRB

named

Begg

B.

Math 207, Section 5 ( online) Exam 1 – Page 6 of 6

  1. (20 points) Consider the following matrices
A= [ 3 -1 ] B = [ 4 1 1 ]
5 2' 123'

Compute each of the following, or say it is not defined and explain why:

(a) (4 points)
2BA

(b) (4 points)
1
2(A-AT)

(c) (4 points)
BET +B

(d) (4 points)
AB-2B
e.--
(.tJ) (4 points)

\
A-

1