Problem 2.8: In example 2.6 (lecture notes), we solved the system Ax = b with
A = [10 5 0
1 5 1
0 -2 -10
-10 1 0]
b = [0
0]
Using elementary row operations, we transformed the matrix [A b] into
[A b] = [1 5 0 0 -1/3
0 0 1 0 1/3
0 0 0 1 8/3]
Hence,
c = [1/3
8/3]
is a particular solution.
a) Use the above particular solution to find the set of all solutions to the system Ax = b.
b) Find another particular solution by working with the last three columns of the matrix A, which are linearly independent. This particular solution has the form (x1, x2, x3) = (0, 2, 3, 4) for some x2, x3.