What Does Triangularizing a Matrix Mean in Linear Algebra?

[kolycholy]

what does triangularizing a matrix mean?
i am supposed to find determinant of a 3 by 3 matrix using big formula, but then I am asked to verify my result by "triangularizing the matrix"
thanks!

 

[HallsofIvy]

Use row operations to reduce the matrix to "upper triangular". That is, a matrix that has only 0's below the main diagonal. You do not need (nor want) to get 1 on the diagonal. If you reduce a matrix to upper triangular using only the row operations of "swap two rows" and "add (or subtract) a multiple of one row to (from) another", and not "multiply (or divide) one row by a number", then the determinant is just the product of the numbers on the main diagonal.