- #1

Illuminerdi

- 30

- 0

Hi, I have a problem from a textbook on control systems along with the solution, but I'm not certain how the answer was derived. The only thing I'm confused by is the method by which the system of equations was solved, which appears to be something similar to, but not quite, Cramer's rule. I've attached the problem and part of the solution.

I began by converting the circuit elements into impedances and then using nodal analysis at each node, the bottom node as ground, to obtain the system of equations, as in the matrix listed. The transfer function is equivalent to Vo(s)/Vin(s).

Now, I can tell that the method isn't Cramer's rule, because, for the equation Ax=b, the b is the zero vector, meaning any determinant replacing a column with it would be equal to zero. For reasons unknown to me, the 1st row and 3rd column were eliminated to create a 2x2 matrix (presumably for which the determinant was calculated) in order to solve for the 3rd variable, and the 1st row and 1st column were removed to similarly solve for the 1st variable. I'm unfamiliar with any reason why these rows and columns were removed, or the procedure as a whole, for that matter.

Thank you for your assistance.

I began by converting the circuit elements into impedances and then using nodal analysis at each node, the bottom node as ground, to obtain the system of equations, as in the matrix listed. The transfer function is equivalent to Vo(s)/Vin(s).

Now, I can tell that the method isn't Cramer's rule, because, for the equation Ax=b, the b is the zero vector, meaning any determinant replacing a column with it would be equal to zero. For reasons unknown to me, the 1st row and 3rd column were eliminated to create a 2x2 matrix (presumably for which the determinant was calculated) in order to solve for the 3rd variable, and the 1st row and 1st column were removed to similarly solve for the 1st variable. I'm unfamiliar with any reason why these rows and columns were removed, or the procedure as a whole, for that matter.

Thank you for your assistance.