Consider the following system of linear equations in variables x,y, and z. x+y-2z=0 2x+y+kz=0 -5x+ky-2z=0 where k is a constant. Which of the following statements is true? (Read them carefully!) The system has a nontrivial solution for any value of k. The system has a nontrivial solution for exactly one value of k. The system is inconsistent for any value of k. The system has a nontrivial solution for exactly two values of k. The system has only the trivial solution for any value of k.
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A nontrivial solution exists if the determinant of the coefficient matrix is zero. ** Show more…
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