document.write( "Question 381653: Evaluate the following determinants.\r
\n" ); document.write( "\n" ); document.write( "This is a 3x3 matrix. the 3 is outside of the matrix.\r
\n" ); document.write( "\n" ); document.write( " |-2 -1 0|
\n" ); document.write( "3 |-3 5 -2|
\n" ); document.write( " | 0 8 -1|\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #270724 by Jk22(389)\"\" \"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%2C-2%2C-1%2C0%2C-3%2C5%2C-2%2C0%2C8%2C-1%29%29\", we can see that \"a=-2\", \"b=-1\", \"c=0\", \"d=-3\", \"e=5\", \"f=-2\", \"g=0\", \"h=8\", and \"i=-1\"

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

\"abs%28matrix%283%2C3%2C-2%2C-1%2C0%2C-3%2C5%2C-2%2C0%2C8%2C-1%29%29=-22--3%2B0\" Multiply

\"abs%28matrix%283%2C3%2C-2%2C-1%2C0%2C-3%2C5%2C-2%2C0%2C8%2C-1%29%29=-19\" Combine like terms.


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Answer:

So \"abs%28matrix%283%2C3%2C-2%2C-1%2C0%2C-3%2C5%2C-2%2C0%2C8%2C-1%29%29=-19\", which means that the determinant of the matrix \"%28matrix%283%2C3%2C-2%2C-1%2C0%2C-3%2C5%2C-2%2C0%2C8%2C-1%29%29\" is -19

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\n" ); document.write( "\n" ); document.write( "The final determinant is 3³*(-19)=the latter, hence : -513.
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\n" ); document.write( "We can compare to the matrix multiplied by 3 :
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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%2C-6%2C-3%2C0%2C-9%2C15%2C-6%2C0%2C24%2C-3%29%29\", we can see that \"a=-6\", \"b=-3\", \"c=0\", \"d=-9\", \"e=15\", \"f=-6\", \"g=0\", \"h=24\", and \"i=-3\"

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

\"abs%28matrix%283%2C3%2C-6%2C-3%2C0%2C-9%2C15%2C-6%2C0%2C24%2C-3%29%29=-594--81%2B0\" Multiply

\"abs%28matrix%283%2C3%2C-6%2C-3%2C0%2C-9%2C15%2C-6%2C0%2C24%2C-3%29%29=-513\" Combine like terms.


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Answer:

So \"abs%28matrix%283%2C3%2C-6%2C-3%2C0%2C-9%2C15%2C-6%2C0%2C24%2C-3%29%29=-513\", which means that the determinant of the matrix \"%28matrix%283%2C3%2C-6%2C-3%2C0%2C-9%2C15%2C-6%2C0%2C24%2C-3%29%29\" is -513
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