SOLUTION: by the examining the determinant of the coefizient matriks, show that the following system has a nontrivial solition if and only if α.β x+y+αz=0 x+y+βz=0 &#9

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Question 1055240: by the examining the determinant of the coefizient matriks, show that the following system has a nontrivial solition if and only if α.β
x+y+αz=0
x+y+βz=0
αx+βy+z=0
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.
The determinant of the matrix is 

 = .


Therefore, the given system has a non-trivial solution if and only if 

 = 0,  or,  equivalently,   = .

Honestly, I don't know what condition on and is written in your post (or what you were going to write there).

Unfortunately.


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