document.write( "Question 955465: Determinant of the matrix
\n" ); document.write( " | 18 40 89 |
\n" ); document.write( " | 40 89 198 |
\n" ); document.write( " | 89 198 440 |
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Algebra.Com's Answer #583695 by MathLover1(20850)\"\" \"About 
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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
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