# 代写math – math207, Section 5

### math207, Section 5 `````` 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*-

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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
(d) (3 points) In ~art (b), for this particular choice of vector b, how many solutions
``````
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``````

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``````)(
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``````

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DeBeers

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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
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``````

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-
``````

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