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Past Exam for MATH 233 - Elementary Linear Algebra at SUNY at Geneseo (SUNY Geneseo)
Exam Information
| Material Type: | Final |
| Professor: | Staff |
| Class: | MATH 233 - Elementary Linear Algebra |
| Subject: | Mathematics |
| University: | SUNY at Geneseo |
| Term: | Spring 2006 |
| Keywords: |
|
Sample Document Text
Linear Algebra MA233
1. Let T:R5 !R3 be a MAP THAT WE WOULD LIKE TO BE a linear transformation.
Let T(v1) = u1; T(v2) = u2; T(v3) = u3; T(v4) = u4; T(v5) = u5:
Let v1 =
2
66
66
4
1
0
0
0
0
3
77
77
5
;v2 =
2
66
66
4
1
1
0
0
0
3
77
77
5
;v3 =
2
66
66
4
1
2
1
0
0
3
77
77
5
;v4 =
2
66
66
4
2
3
1
4
2
3
77
77
5
;v5 =
2
66
66
4
2
1
2
B
2
3
77
77
5
:
Let u1 =
2
4
1
1
2
3
5; u2 =
2
4
2
2
1
3
5; u3 =
2
4
2
3
2
3
5;u4 =
2
4
2
2
4
3
5 u5 =
2
4
1
5
0
3
5
(a) Show that B can be 0.
(b) What value(s) can’t B be? Give a valid reason.
2. Let T:R5 !R3 be a linear transformation.
Let T(v1) = u1; T(v2) = u2; T(v3) = u3; T(v4) = u4; T(v5) = u5:
Let v1 =
2
66
66
4
1
0
0
0
0
3
77
77
5
;v2 =
2
66
66
4
1
1
0
0
0
3
77
77
5
;v3 =
2
66
66
4
1
2
1
0
0
3
77
77
5
;v4 =
2
66
66
4
2
3
1
4
2
3
77
77
5
;v5 =
2
66
66
4
2
1
2
0
2
3
77
77
5
:
Let u1 =
2
4
1...
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