Question

KVL equations of circuit can be written as

10I ₁−2I ₂−5I ₃=25
−2I ₁+13I₂ −1I ₃=2
−5V ₁−V ₂+10I ₃=15
d) Write is in form of A⋅X=b and solve it with LU decomposition method
a. Decompose the coefficient matrix as L and U

Answer 1

The given KVL equations of the circuit can be rearranged and written in the form of A⋅X=b. We can then decompose the coefficient matrix A into lower and upper triangular matrices L and U. The LU decomposition of A is L = [1 0 0; 0.2 1 0; -0.5 0.051 1] and U = [10 -2 -5; 0 13.4 -0.6; 0 0 9.61]. finally, we can solve the system of equations using the LU decomposition method.

Step-by-step explanation:

The given equations represent the Kirchhoff's Voltage Law (KVL) equations of a circuit. In order to write them in the form of A⋅X=b and solve them using the LU decomposition method, we need to rearrange the equations. The coefficient matrix A will be formed by the coefficients of the unknown currents, and the vector b will contain the constants on the right-hand side of the equations.

After rearranging the equations, the coefficient matrix A is:

10 -2 -5
-2 13 -1
-5 -1 10

The vector b is:

25
2
15

Now, we can decompose the coefficient matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. the LU decomposition of A is:

L =

1 0 0
0.2 1 0
-0.5 0.051 1

U =

10 -2 -5
0 13.4 -0.6
0 0 9.61

Finally, we can solve the system of equations using the LU decomposition method.