How Do Row Operations Affect a Determinant's Value?

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Row operations can significantly affect the value of a determinant, particularly when a row is replaced by a nonzero multiple of itself or when two rows are swapped. In the discussed matrix evaluation, an error occurred during the row operations, leading to a discrepancy between the calculated and actual determinant values. The correct determinant value for the matrix in question is -17. Understanding how these operations influence the determinant is crucial for accurate calculations. Proper application of row operations is essential for obtaining the correct determinant.
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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.
 
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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.
 

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