matrices - Check the determinant of a matrix given a parameter

• How do I calculate the determinant of the following matrix?


• And for which values of m is the determinant non null?

\begin{bmatrix}
1 & 1 & 1 \\
2 & m & 3 \\
4 & m^2 & 9

\end{bmatrix}
I have tried the

co-factoring method

and what I got was m(m+1) + 6
I'm trying to figure what would be the right way to do this?

Answer

In general, you can calculate the determinant of any 3x3 matrix with the method described in the introductory section of the corresponding wikipedia article.

After you have successfully calculated the determinant (-m^2 + 5 m - 6), determine the zeros of this quadratic equation depending on m. Except for these two values of m the determinant will be non-zero.