Assume that it takes one second to factorize $500 \times 500$ matrix $A$ into $A = LU$. How many problems $Ax = b_1, … , Ax = b_k$ can be solved in the same time?
Here are my workings, this is the first time doing this sort of calculation so I am not sure if my workings are correct or not. Looking for some confirmation and help with this.
The two back substitutions for each $b_i$ require a total of $2n^2$ operations. Therefore, the approximate number of $b_i$ that can be handled per second is
$$\frac{\frac{2n^3}{3}}{2n^2} = \frac{n}{3} = \frac{500}{3} = 166.666....$$