Math 205a Quiz 02 Worksheet - Bates College - 2007
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1Math 205A
Quiz 02, page 1
September 21, 2007
NAME
3
1 3
5
6
1
1. Find
0 1
3
2
.
0
2 5
7 10
2
2. Let A be the 3 × 4 matrix from problem 1. Express all solutions of Ax = b in the form p + v
,
h
where p is a particular solution of Ax = b and v
represents all solutions to the corresponding
h
70
.
20
homogeneous equation Ax = 0. Here, b =
120
1 0
4 0 10
is row equivalent to the augmented matrix you would set up to begin
Hint.
0 1
3 2 20
0 0
0 0
0
solving this problem.
3. Let A and b be as in problem 2. Let a
, a
, a
and a
be the columns of A. Use your answer
1
2
3
4
to (2) to express b as a linear combination of a
, a
, a
and a
in 3 different ways, the first of which
1
2
3
4
should be by setting all free variables to 0. Make clear your choices of values for the free variables.
(See on-board example).
LC 1:
LC 2:
LC 3:
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