Math 205B Quiz 02 page 1 01/22/2010 Name
Note: On this quiz, use the appropriate notation (e.g. “vector hats”) wherever appropriate. Also, show any rref’s you
use in any problem that requires one.
1. Suppose that Ais a 4 ×6 matrix, and consider the matrix equation Ax=b.
1A. How many rows does Ahave?
1B. How many columns does Ahave?
1C. The vector xbelongs to Rhfor what value of h?
1D. The vector bbelongs to Rpfor what value of p?
2. Suppose that A=
3 1 1 5
4 2 2 8
4 1 3 8
1 2 2 5
. Let z=
1
1
1
0
,b=
3
2
1
0
and d=
7
10
7
4
.
Label column vectors of Aas a1,a2,a3, and a4.
2A. Find the linear combination of a1,a2,a3, and a4represented by Az.
2B. Can bbe expressed as a linear combination of a1,a2,a3, and a4? Explain why or why not.
2C. Find all solutions xof the matrix equation Ax=d.
2D. Do the column vectors of Aspan R4? Explain.