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 0012Explanation / 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
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