Gaussian Elimination with partial pivoting
(a) Show that the matrix
A = [ 0.1 0.2 0.3 ]
[ 0.4 0.5 0.6 ]
[ 0.7 0.8 0.9 ]
is singular. That is, find a nonzero vector such that Ay = 0, y ≠ 0. Describe the set of solutions for Ax = b if
b = [0.1]
[0.3]
[0.5]
Note that one solution is x = [7/18;4/18;1/18]