Math 205A Quiz 02 page 1 January 18, 2008 NAME
x1+2x2+4x3=21
1.Consider the system of equations 4x1+7x2+13x3=72
3x1+4x2+6x3=39.
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!
2. Let v1=
1
4
3
,v2=
2
7
4
,v3=
4
13
6
, and b=
21
72
39
.
2A. If possible, express the vector bas a linear combinations of the vectors v1,v2, and v3in two different
ways, or explain why this cannot be done.
2B. Is c=
22
73
40
in the span of v1,v2, and v3? Fully explain your answer. Write down any matrices
which support your conclusion.