SOLUTION: HI. I am having a little trouble with the 3x3 determinants. I have got the 2x2 down just fine. Here is my problem. -5 -3 2 second row 8 0 7 third row 3 2 -6. I know that I have to

Question 222462: HI. I am having a little trouble with the 3x3 determinants. I have got the 2x2 down just fine. Here is my problem. -5 -3 2 second row 8 0 7 third row 3 2 -6. I know that I have to cancel row 1 and column 1 and solve the 2x2, but then what? Any help is greatly appreciated! Thanks!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix

If you have the general 3x3 matrix:

the determinant is:

Which further breaks down to:

Note: , and are determinants themselves.
If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver

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From the matrix , we can see that , , , , , , , , and

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

Multiply

Combine like terms.

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Answer:

So , which means that the determinant of the matrix is -105

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