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X1-3x2 + 2x3 = 0 2x1-5x2 + 3x3 = 0 3x1-8x2 + tx3 = 0 t =? General solution of homogeneous matrix
Coefficient matrix A=
1 -3 2
2 -5 3
3 -8 t
r2-2r1,r3-3r1
1 -3 2
0 1 -1
0 1 t-6
r1+3r2,r3-r2
1 0 -1
0 1 -1
0 0 t-5
When t ≠ 5, the equations have only zero solutions
When t = 5
A-->
1 0 -1
0 1 -1
0 0 0
The general solution of the equations is K (1,1,1) ^ t
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