101k views
2 votes
Show the matrix A and vector b and then solve for V1 and V2 in polar formats

V1−4∠30°/5+10i + V1−V2/−15i=3∠40°
−10iV1+V1−V2/8+3=0

User Kymberlee
by
8.4k points

1 Answer

3 votes

Final answer:

To solve for V1 and V2 in polar format, rewrite the equation in matrix form Av = b, where A is a square matrix. Invert matrix A, multiply the inverse of A with vector b to obtain the solution for v. The resulting values for V1 and V2 will be in polar format.

Step-by-step explanation:

To solve for V1 and V2 in polar format, we need to first identify the matrix A and the vector b.

From the given equation: V1−4∠30°/5+10i + V1−V2/−15i=3∠40°−10iV1+V1−V2/8+3=0, we can rewrite the equation in matrix form: Av = b, where v is the column vector [V1, V2] and A is a square matrix.

After organizing the equation in matrix form, we can perform matrix multiplication to solve for v. First, invert the matrix A. Then, multiply the inverse of A with the vector b to obtain the solution for v. The resulting values for V1 and V2 will be in polar format.

User Giraff
by
8.0k points