SOLUTION: I want solution I am trying a lot Derminant of 3×3 matrix 18 40 89 40 89 198 89 198 440

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Question 955472: I want solution I am trying a lot
Derminant of 3×3 matrix
18 40 89
40 89 198
89 198 440
Answer by MathLover1(20849) About Me  (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:

%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

the determinant is:

Which further breaks down to:



Note: abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29, abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29 and abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 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 %28matrix%283%2C3%2C18%2C40%2C89%2C40%2C89%2C198%2C89%2C198%2C440%29%29, we can see that a=18, b=40, c=89, d=40, e=89, f=198, g=89, h=198, and i=440

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C18%2C40%2C89%2C40%2C89%2C198%2C89%2C198%2C440%29%29=-792--880%2B-89 Multiply

abs%28matrix%283%2C3%2C18%2C40%2C89%2C40%2C89%2C198%2C89%2C198%2C440%29%29=-1 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C18%2C40%2C89%2C40%2C89%2C198%2C89%2C198%2C440%29%29=-1, which means that the determinant of the matrix %28matrix%283%2C3%2C18%2C40%2C89%2C40%2C89%2C198%2C89%2C198%2C440%29%29 is -1