Math 205A Quiz 02 page 1 September 19, 2008 NAME
1. Let A=
52−512
61−13 13
−20 6 −4
and let b=
b1
b2
b3
.
1A. Use the “super-augmented” matrix technique discussed in class to find what conditions (if any)
there are on b1,b2, and b3which guarantee that Ax=bhas a solution.
1B. What value must b1have to ensure that w=
b1
−13
12
can be written as a linear combination of the
columns of A?
1C. Express wfrom (1B) as a specific linear combination of the columns a1,a2,etc. of A. Your answer
will have the form “w=x1a1+x2a2+...
00 (etc) where you’ll supply the actual values of x1,x2,etc..
1D. Let z=
43
11
6
. Express all solutions of Ax=zin the form p+vhwhere pis a particular solution
of Ax=zand vhrepresents all solutions of Ax=0.
1E. Explicitly give the “trivial solution” of Ax=0.