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Systems of Three Equations
Terms
Introduction and Summary
Terms
Solving by Addition and Subtraction
Problems
Solving using Matrices and Row Reduction
Problems
Solving using Matrices and Cramer's Rule
Problems
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Introduction and Summary
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Solving by Addition and Subtraction
Systems of Three Equations
Terms
Determinant
-
Of a
2×2
matrix
:
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
=
y
=
z
=
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
.
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