document.write( "Question 175934: find the coefficient matrix and evalute its determinant.
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Algebra.Com's Answer #131042 by jim_thompson5910(35256) $\"\"$ $\"About$

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Since the coefficients are 9,-2, 3, and 2, this means that the coefficient matrix is $\"%28matrix%282%2C2%2C+9%2C-2%2C+3%2C2%29%29\"$ \r
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Solved by pluggable solver: Finding the Determinant of a 2x2 Matrix

If you have the general 2x2 matrix:

$\"%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\"$

the determinant is: $\"D=a%2Ad-c%2Ab\"$

So this means that

$\"abs%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29=a%2Ad-c%2Ab\"$

Note: the vertical bars denote a determinant.

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So in this case the determinant of $\"%28matrix%282%2C2%2C9%2C-2%2C3%2C2%29%29\"$ is:

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$\"abs%28matrix%282%2C2%2C9%2C-2%2C3%2C2%29%29=%289%29%282%29-%283%29%28-2%29=18--6=24\"$

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Answer:

So $\"abs%28matrix%282%2C2%2C9%2C-2%2C3%2C2%29%29=24\"$ which means that the determinant of the matrix $\"%28matrix%282%2C2%2C9%2C-2%2C3%2C2%29%29\"$ is 24

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