SOLUTION: find the coefficient matrix and evalute its determinant. 9x-2y=15 3x+2y=5

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Question 175934: find the coefficient matrix and evalute its determinant.
9x-2y=15
3x+2y=5
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the coefficient matrix and evalute its determinant.
9x-2y=15
3x+2y=5
------------------
9...-2
3....2
-----------------
D = 18 - -6 = 24
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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


Determinant:

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:


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