I am really confused and frustrated i put this matrix in a calculator and found the determinant to be 9 but when i do the math myself i get -11? What am i doing wrong here?? Here is the matrix:
1 -2 1
2 2 -1
1 -1 2
by using the diagonals method.
to do this, write like this:
You multiply the first element by the one on the down sloping diagonal, and so forth.
element (1,1) * element (2,2) * element (3,3)
element (2,1) * element (3,2) * element (4,3)
and so on.
When you go up a diagonal, you subtract the product from the total.
Hope this helps!
That method, unfortunately, only works for 3 by 3 determinants.
Another way to do it- expand by minors on the first row:
Yet another- row reduce:
Subtract twice the first row from the second row and subtract the first row from the third row to get
Swap the second and third rows, then subtract 6 times that new second row from the new third row to get
Adding (or subtracting) a multiple of one row from another does not change the determinant and swapping two rows multiplies the determinant by -1 so the determinant of the original matrix is -1 times the determinant of this "upper triangular matrix".
(Multiplying or dividing one row by a number, a row operation not used here, multiplies of divides the determinant by that number.)