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

Thanks

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- November 16th 2009, 04:28 PMnascar77Determinant of a 3X3 matrix
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

Thanks - November 16th 2009, 04:30 PMKrizalid
bet you show your work and we'll spot what you're doing wrong.

- November 16th 2009, 08:49 PMbictory

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! - November 17th 2009, 06:01 AMHallsofIvy
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.)