Math 205A Quiz 01 page 1 January 11, 2008 NAME
1. By hand, find a matrix in RREF which is row equivalent to the following matrix. Show and label all
your steps as we’ve done in class, for example, if you add 4 copies of row 5 to row 8, write “r8←r8+4r5”;
if you swap rows 4 and 5, write “swap r4and r5”, etc. (you don’t need the quotes) Use steps that make
the work easy.
40 1 2 2000 6042
000 10 30
1 0 0 50 151
2. Suppose an augmented matrix is in RREF and one of its rows is 0 0 0 0 1.
2A: Can there be any rows below this one in that augmented matrix? Explain.
2B: Does the underlying system of equations have no solutions, one, or infinitely many? Fully explain
your answer.
3. Suppose the augmented matrix corresponding to some system of equations is row equivalent to
10−203
01 500
00 011
3A: What are the solutions? (Express them in terms of any free variables)
3B: What are the pivot columns of this matrix? Use notation like c1,c2,c3etc.