Determinant of 4 x 4

1. Jun 26, 2008

rocomath

Ok, I have gotten different answers by reducing to an upper triangle, co-factor, and my calculator. All 3 giving me different answers!

|Upper-triangle| = lol, was looking at the wrong problem ... I did get 36.
|Co-factor reduction mobob| = uh i keep messing it up
|Calculator| = 36

1 2 3 0
2 6 6 1
-1 0 0 3
0 2 0 7

Expanding using row 3

(a)
-1
2 3 0
6 6 1
2 0 7

(b)
-3
1 2 3
2 6 6
0 2 0

Expanding once again to reduce it to a 2 x 2

(a)
-1 times determinant of these 2 x 2

2
3 0
6 1

7
2 3
6 6

(b)
-3

-2
1 3
2 6

Last edited: Jun 26, 2008
2. Jun 26, 2008

Dick

Maxima, the free computer software of my choice, says 36. Doing it by hand the determinant of your first 3x3 is -36. The determinant of the second 3x3 is 0.

Last edited: Jun 26, 2008
3. Jun 26, 2008

rocomath

Ok the book answer has to be wrong then.

4. Jun 26, 2008

Dick

I really think it is 36.

5. Jun 26, 2008

HallsofIvy

Staff Emeritus
"Row reduction" reduces that matrix to
$$\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\0 & 2 & 0 & 1 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 6$$
and the product along the diagonal is 36.