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

Algebra ->  Matrices-and-determiminant -> 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      Log On

The determinant of the matrix is 

 = .


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

 = 0,  or,  equivalently,   = .