SOLUTION: Determinant of the matrix | 18 40 89 | | 40 89 198 | | 89 198 440 |

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Question 955465: Determinant of the matrix
| 18 40 89 |
| 40 89 198 |
| 89 198 440 |
Answer by MathLover1(20850)   (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 -1
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