document.write( "Question 955472: I want solution I am trying a lot
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\n" ); document.write( " 18 40 89
\n" ); document.write( " 40 89 198
\n" ); document.write( " 89 198 440 \n" ); document.write( "

Algebra.Com's Answer #583692 by MathLover1(20849) $\"\"$ $\"About$

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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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