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Homework Statement
Matrix U is the following matrix:
http://www.wolframalpha.com/input/?i={{a,b,c},{0,d,e},{0,0,f}}
Question:
If a, d, f are all nonzero, show that the only solution to Ux = 0 is x = 0. Then the upper triangular matrix U has independent columns.
The solution says:
xcomplete = xparticular + xhomogeneous = (1/2,0,1/2,0) + x2 (-3,1,0,0) + x4(0,0,-2,1)
Homework Equations
xcomplete = xparticular + xhomogeneous
The Attempt at a Solution
I'm very confused; I'm not sure where to start.
Any help in figuring out what I need to do would be really appreciated!