Matrix
Algebra
Level
3
The system of linear equations
has a non-trivial solution for
exactly one values of
exactly two values of
exactly three values of
infinitely many values of
insufficient information
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1 solution
If the matrix ⎝ ⎛ 1 γ 1 γ − 1 1 − 1 − 1 − γ ⎠ ⎞ is invertible, there is a unique solution, but it would be the trivial one. For another solution to exist, the matrix must not be invertible. This append when the determinant of the matrix is 0.
∣ ∣ ∣ ∣ ∣ ∣ 1 γ 1 γ − 1 1 − 1 − 1 − γ ∣ ∣ ∣ ∣ ∣ ∣ = ( γ − 1 ) γ ( γ + 1 ) = 0 . There are three values of γ .