How Do You Calculate the Determinant of a 5x5 Matrix?

[babygirl_28]

i have a problem that i need to find the determinant of a 5x5 matrix. i have no clue how to go about solving this problem

2, -9, 1, 8, 4
-10, -1, 2, 7, 0
0, 4, -6, 1, -8
6, -14, 11, 0, 3
5, 1, -3, 2, -1

 

[micromass]

i have a problem that i need to find the determinant of a 5x5 matrix. i have no clue how to go about solving this problem

2, -9, 1, 8, 4
-10, -1, 2, 7, 0
0, 4, -6, 1, -8
6, -14, 11, 0, 3
5, 1, -3, 2, -1

What's the definition of a determinant?? What theorems did you see??

 

[iRaid]

http://people.richland.edu/james/lecture/m116/matrices/determinant.html
Go like all the way down

 

[HallsofIvy]

There are a number of different ways to calculate a determinant. The method I personally prefer is to row-reduce a triangular matrix. As long as you use only "add a multiple of one row to another", you wil always have matrices with the same determinant. And the determinant of a triangular matrix is just the product of the numbers on the diagonal. Of course, if you get a "0" on the diagonal, you can stop- the determinant is 0.

You never have to use "swap two rows" or "multiply/divide a row by a number" but if you do to simplify the arithmetic, whenever you swap two rows, you need to multiply the final result by -1 to get the correct determinant and whenever you multiply/divide a row by a number, you need to divide/multiply the row by that number to get back to the correct determinant.

 

[DuncanM]

Do you need a numerical answer?
If so, there are many free calculators available that would do it.

Or do you need to work through all the steps of its computation?
If you've been asked to do something, you should have been first taught the technique for doing so. If not, the reference already recommended, plus Wikipedia or MathWorld, offer good introductory material.