I have to find the determinant of this matrix using different properties of the determinant. We can not simply give the solution by finding it with mathematics sotware.
I have tried puting it into reduced row echelon form, but this takes ages.Is there an easier way?
Q1)Show that the determinant of the following matrix is
Denote the mentioned matrix by . Now, note that , meaning is an eigenvalue of geometric multiplicity 4 -> algebraic multiplicity .
Now, use the fact that for any matrix A, where are the eigenvalues of A:
In this case, we have that .
Finally, using the fact that , we get