Math Worksheets - 205b And C Quiz 02
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1Math 205B&C Quiz 02 page 1 01/30/09
Name
Section: 8am
1:10 pm
2
5 10
6 12
11
1 0 5 0
6
7
1
2
5
3
6
7
0 1 0 0
0
3
Let A =
and b =
; then RREF of [A|b] is
.
3 10 15
8 14
7
0 0 0 1
4
2
1
3
5
2
2
2
0 0 0 0
0
0
1A. Use the above information to express all solutions of Ax = b in the form p + v
where p is a
h
particular solution of Ax = b and v
represents all solutions of the corresponding homogeneous equation.
h
1B. In terms of the definition of linearly independent, do the columns of A form a linearly independent
set? Explain your answer.
1C. Label the columns of A as a
, a
, . . . , a
. Show explicitly how to express a
as a linear combination
1
2
5
5
of the first four columns. Give two different ways to do this, one of which involves a non-zero weight for
column a
, while the other does not use a
(ie, its weight is 0).
3
3
(Write your answers using the symbols a
, a
, . . . , a
; don’t copy over all those columns of numbers).
1
2
5
1D. Explain why column a
can not be written as linear combination of the other four columns.
2
4
1E. Do the columns of A span R
? Why or why not.
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