Math 314 Final Exam Spring, 1996
Math 314 Final Exam Spring, 1996
Math 314 Final Exam Spring, 1996
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⎡1 2 −1 1⎤<br />
3.(24 pts) Given that A =<br />
⎢<br />
2 4 −3 0<br />
⎥<br />
has row echelon form<br />
⎢<br />
⎥<br />
U<br />
⎢⎣1 2 1 5⎥⎦<br />
⎡1 2 −1 1⎤<br />
=<br />
⎢<br />
0 0 1 2<br />
⎥<br />
⎢ ⎥<br />
⎢⎣<br />
0 0 0 0⎥⎦<br />
(a) Find a basis for the null space of A.<br />
(b) Find a basis for the range of A.<br />
(c) Find a basis for the row space of A.<br />
(d) Determine rank ( A)<br />
.<br />
4.(28 pts) True or false. Please explain your answer.
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