Example 2 - Use Cramer's Rule to express the solution of a system in Determinant Form

Example:
Analysis of a certain DC network results
Use Cramer's Rules to solve for V₁ and V₂ in the system of equations below:

  0.75 V₁  - 0.25 V₂ = 1
-0.25 V₁  + 0.75 V₂ = -2

Solution:
Note: This example illustrate how Cramer's Rules avoids having to deal with fractions that would result if the system was solved by other methods...

Solve with Cramer's Rule...
System determinant
∆ =

0.75	-0.25
-0.25	0.75

= (0.75) (0.75) - (-0.25) (-0.25) = 0.50

∆ = 0.50

∆₁ =

1	-0.25
-2	0.75

= (1) (0.75) - (-0.25) (-2) = 0.25

∆₁ = 0.25

∆₂ =

0.75	1
-0.25	-2

= (0.75) (-2) - (1) (-0.25) = -1.25

∆₂ = -1.25

Finally, by Cramer's Rule...

V₁  = ∆₁ / ∆ = 0.25 / 0.50 = 0.50
V₂ = ∆₂ / ∆ = -1.25 / 0.50 = -2.5

Note: Nice features of this method of solution: seems easy to solve... no fractions...
Can solve for one variable at a time.