How do you find the determinant of #((3, 5, 0, 6), (2, 3, 2, 0), (2, 4, 0, 7), (-3, 2, 2, 3))#?
I would try to simplify a bit our original matrix to get a line or column of all zeroes but one number.
One column that seems good in this sense is the third one where we have two zeroes already!
Now, I can multiply the second line by
the second line would become:
we add this line to the third and we get:
we see that the third column has 3 zeroes and only one number: we can cancel the column and line crossing at
The determinant can be now "easily" evaluated using Laplace or Sarrus to get: