System of equations
Algebra
Level
4
If the system of linear equations above has a non-trivial solution, then choose the most precise option.
It is true for infinitely many values of
It is true for exactly two values of
It is true for exactly one values of
It is true for exactly three values of
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1 solution
Because the system of equations is homogeneous (i.e. for every value of k there is always at least one solution (x,y,z) = (0,0,0), it suffices to calculate the roots of the determinant. Det(k) =k³-k which has roots -1,0 and 1, there are 3 such valus of k.