1. Homework Statement
I have to prove that the expression
$$\frac{\omega C - \frac{1}{\omega L}}{\omega C - \frac{1}{\omega L} + \omega L - \frac{1}{\omega C}}$$
is equal to
$$\frac{1}{3-( (\frac{\omega_r}{\omega})^2 + (\frac{\omega}{\omega_r})^2)}$$
where ##\omega_r= \frac{1}{\sqrt{LC}}##...
So what I did was:
I took the square of the length:
$$ (x_1)^2 + \frac {2}{9} + \frac {2}{3} x_1 $$
And then I calculated the 1st derivative of this expression and zero gave me value for x_1: -8/3
I made a substitution of this value in my original expression and I got my solution
Thanks for the reply!
So in that case I need to minimize the square of the length of (x_1, \frac{1}{3}, \frac{1}{3} + x_1) right? Because if I minimize the square length of (x_1, 0, x_1) I reach to a zero solution, right?
Than I can write that the family of the least squares solution is...
1. Homework Statement
In R^3 with inner product calculate all the least square solutions, and choose the one with shorter length, of the system:
x + y + z = 1
x + z = 0
y = 0
2. The attempt at a solution
So I applied the formula A^T A x = A^T b with A as being the matrix with row 1...