Equation Worksheets - Math 205a - 2008
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1Math 205A
Quiz 02 page 1
January 18, 2008
NAME
x
+ 2x
+4x
= 21
1
2
3
1. Consider the system of equations
4x
+ 7x
+13x
= 72
1
2
3
3x
+ 4x
+6x
= 39.
1
2
3
1A. Use your calculator to find the RREF of the augmented matrix corresponding to this system and
write the answer here.
1B. What does the answer to (1A) tell us the solution to the system is? (Answer using the standard
notation developed in class)
1C. Suppose the “4” in the third equation in the above system is replaced by a “5”. What is the RREF
of the augmented matrix corresponding to this new system?
1D. What is the solution of the new system described in part (1C)? Verify that it works!
1
2
4
21
, v
, v
, and b =
.
2. Let v
=
4
=
7
=
13
72
1
2
3
3
4
6
39
2A. If possible, express the vector b as a linear combinations of the vectors v
, v
, and v
in two different
1
2
3
ways, or explain why this cannot be done.
22
in the span of v
2B. Is c =
73
, v
, and v
? Fully explain your answer. Write down any matrices
1
2
3
40
which support your conclusion.
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