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MAT 242 Spring2018: import × 242h3.pdf https://mathcms2.asu.edu/moodle/pluginfil

ID: 3136712 • Letter: M

Question

MAT 242 Spring2018: import × 242h3.pdf https://mathcms2.asu.edu/moodle/pluginfile.php/27894/mod pag | | a search - + Automatic Zoom : MAT 242 Written Homework #3 EP4.2, 4.3/ H4.2, 4.3 Solve the following problems, showing any necessary work. Due: February 28 March 14 | 1 , 1-: 1 , 1 3 1. [1 point] Let W be the subspace spanned by Which of the following vectors are in W? (Note that the number of correct answers might be zero, one, two, three, or four.) -191 29 171 r-37 2027 90- 26 301.1 77 -4030 linearly dependent. Find a nontrivial linear combination of these vectors that adds up to Ö. 2 1 F5 ES 2612 C 3222 3333i 1300 0012

Explanation / Answer

1.Let A =

-3

3

0

17

-37

-30

-19

-1

-2

3

20

-27

26

29

-1

2

-3

90

-40

-30

77

3

2

1

14

-2

-6

-3

The RREF of A is

1

0

0

0

712/97

2

-66/97

0

1

0

0

-147/194

-8

-1502/97

0

0

1

0

-1168/97

4

881/97

0

0

0

1

-145/194

0

145/97

Now, it is apparent that only the vector (-30,26,-30,-6)T is in W. The answer is one.

2. Let A = [ v1,v2,v3,v4] =

0

-1

-3

2

0

-3

3

6

1

0

-3

-1

2

0

3

-2

The RREF of A is

1

0

0

-1

0

1

0

-2

0

0

1

0

0

0

0

0

Now, it is apparent that v4 = -v1-2v2 +0v3 so that -v1-2v2 +0v3 –v4 = 0 or, v1+2v2 +0v3 +v4 = 0

-3

3

0

17

-37

-30

-19

-1

-2

3

20

-27

26

29

-1

2

-3

90

-40

-30

77

3

2

1

14

-2

-6

-3