SOLUTION: Evaluate the determinant: |3 3 4| |6 1 2| |3 2 2|

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Question 274498: Evaluate the determinant:
|3 3 4|
|6 1 2|
|3 2 2|
Found 2 solutions by jim_thompson5910, kensson:
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 12
Answer by kensson(21)   (Show Source): You can put this solution on YOUR website!
A neat way of doing this is as follows: write the first two columns again on the right and draw a line down the first three forward diagonals:

3 3 4 3 3
 \ \ \
6 1 2 6 1
   \ \ \
3 2 2 3 2
Multiply down each diagonal and add them up: 6 + 18 + 48 = 72
Now do the same with the last three backward diagonals:

3 3 4 3 3
   / / /
6 1 2 6 1
 / / /
3 2 2 3 2
You get 12 + 12 + 36 = 60
The determinant is the first (72) minus the second (60), giving 12.
For a square matrix of size n, you repeat the first (n-1) columns and use the first and last n diagonals.
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