Originally Posted by

**berni1984** Hello,

I can help you with the first one. For a system of equations to be consistent (with either one or infinite solutions) it has to be satisfied that

$\displaystyle \det\left(\bf A\right)\neq 0$

For this reason, calculating the determinant of the coefficient matrix, you can determine the values of k where the system is not defined:

$\displaystyle \det\left(\bf A\right) = \left|\begin{matrix}1 & 1 & 7 \\ 2 & 3 & 17 \\ 1 & 2 & k^2 + 1 \end{matrix}\right|=k^2 -9=0$

Thus,

$\displaystyle k=\pm 3$ makes the determinant to be equal to zero, and thus, the system is not defined.