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Name
20 Aprl 2006
Teaching Assistant
Hour Test 3
Math 1502J Andrew
Instructions:
1.
Closed book.
2.
Show your work and explain your answers and reasoning.
3.
Calculators may be used, but pay particular attention to instruction 2.
To receive credit, you must show your work.
Unexplained answers,
and answers not supported by the work you show, will not receive
credit.
4.
Express your answers in simplified form.
1.
(25)
Find a basis for the image and a basis for the kernel of the matrix

=
3
0
2
2
1
2
2
1
0
0
4
0
3
4
2
1
0
1
2
1
A
.
Compute the dimension of the image and the dimension of the kernel.
2.
(25)
Find the QR factorization of the matrix
=
4
2
1
0
2
2
2
0
1
A
by applying the Gram
Schmidt process to the columns of
A
.
3.
(25)
A matrix
A
has QR factorization




=
=
1
0
3
2
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
R
Q
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This note was uploaded on 04/07/2008 for the course MATH 1502 taught by Professor Mcclain during the Fall '07 term at Georgia Institute of Technology.
 Fall '07
 McClain
 Math

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