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Cramer's Rule Procedures
Consider a system of two equations in two variables
a11x1 + a12x2 = b1
a21x1 + a22x2 = b2
Cramer's rule:
Solution of the system of equations in two unknowns
is given by the formulas
x1 = det(D1)/det(D)
x2 = det(D2)/det(D)
where det(D1) is the determinant of matrix D1
det(D2) is the determinant of matrix D2
det(D) is the determinant of matrix D
Zero denumerator
Cramer's rule will fail when det(D)=0. The lines associated
with the two equations are parallel in this case. They can be either different
(inconsistent system) when det(D1)=det(D2)=0, or identical
(dependent system) when numerators are not zero.
Cramer's rule
can be also stated as follows:
When a11a22 - a12a21
does not equal 0, then
x1 = b1a22 -
b2a12 / a11a22 -
a12a21
x2 = b2a11 -
b1a21 / a11a22 -
a12a21
The determinant of the matrix A
is defined as det(A) = ad-bc
Example:
matrix(A) =
has the determinant det(A) = (1)(4) - (2)(3) = -2.
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