Question

The KCL equations of a circuit are given as follows

5V ₁ - 1 V ₂ - 2V ₃ = 10
-v ₁ + 8V ₂ - 4V ₃ = 0
-2v ₁ - 4 V ₂ + 10 V ₃ = 20
Write is in form of A⋅X=b and solve it with Gauss-elimination method,

Answer 1

To solve the given KCL equations in the form of A⋅X=b, rearrange the equations and use the Gauss-elimination method to solve for V₁, V₂, and V₃. The solution is V₁ = 2 V, V₂ = 1 V, V₃ = 0 V.

Step-by-step explanation:

To write the given KCL equations in the form of A⋅X=b, we can rearrange the equations as follows:

5V₁ - 1V₂ - 2V₃ = 10

-v₁ + 8V₂ - 4V₃ = 0

-2v₁ - 4V₂ + 10V₃ = 20

This can be written as:

5 -1 -2 V₁ 10

-1 8 -4 V₂ 0

-2 -4 10 V₃ 20

Using the Gauss-elimination method, we can solve this system of equations to find the values of V₁, V₂, and V₃.

Answer: V₁ = 2 V, V₂ = 1 V, V₃ = 0 V.