Determine values of the constant k for which vectors are linearly independent?
Determine all values of the constant k for which the given set of vectors is linearly independent in R4.
So far, I have the system of equations:
Now, the determinant of the coefficient matrix yields 2(k+1)(2-k).
Here is my question: How does the determinant of the coefficient matrix allow me to deduce that "the system has only the trivial solution, and the vectors are linearly dependent if and only if k=-1 or 2"?
Thanks for the help! :)