How Do Row Operations Affect a Determinant's Value?

[_Bd_]

Homework Statement

Evaluate the following determinant by expressing the matrix in upper triangular form.

Homework Equations

row operations.

The Attempt at a Solution

http://yfrog.com/jnscan0001ugj
http://img707.imageshack.us/img707/6379/scan0001ug.jpg
[PLAIN]http://img707.imageshack.us/img707/6379/scan0001ug.jpg

I want to know what I did wrong there cause I can't figure it out
the calculator shows a different answer.

 

[Mark44]

In your 4th (or so) step, you replaced row 2 by 1/2 itself. Replacing a row by a nonzero multiple of itself is one row operation that changes the value of the determinant. The other row operation that does this is swapping two rows.

The correct value of the determinant is -17.