Systems of Three Equations
Terms
Determinant
-
Of a
2×2
matrix:
detA = a 1 b 2 - a 2 b 1 .
Of a 3×3 matrix:
detA = (a 1 b 2 c 3 + b 1 c 2 a 3 + c 1 a 2 b 3) - (a 3 b 2 c 1 + b 3 c 2 a 1 + c 3 a 2 b 1)
A = 
|
detA = a 1 b 2 - a 2 b 1 .
Of a 3×3 matrix:
A = 
|
detA = (a 1 b 2 c 3 + b 1 c 2 a 3 + c 1 a 2 b 3) - (a 3 b 2 c 1 + b 3 c 2 a 1 + c 3 a 2 b 1)
Cramer's Rule
-
Cramer's Rule states that:
x =where D is the 3×3 coefficient matrix, and D x , D y , and D z are each the result of substituting the constant column for one of the coefficient columns in D .
y =
z =
