Question 136905
solve the problem by Cramer's Rule using determinants. The problem is: 
3x - 2y+ z = 6
4x -4y + 3z = 0
5x - 4y + z = -5 
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The determinant of the coefficients is:
[-12-16-30]-[-20-36-8] = -58--64 = 6
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Replace the "x-column" with the constant column to get:
6...-2...1
0...-4...3
-5..-4...1
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The determinant of that 3 x 3 matrix is:
[-24+0+30)-(20+-72+0) = 6--52= 58
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Divide the x-determinant by the coefficient determinant to get x = 58/6=29/3
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To find "y":
1st:Replace the "y-column" in the coefficient matrix by the constant column.
2nd:Find the determinant of this matrix
3rd:Divide that value by 6 to get the value of "y".
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Follow the same pattern for "z".
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Final answer:
x = 29/6
y = 91/6
z = 44/6
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Cheers,
Stan H.