§ Kernel, cokernel, image
Consider a linear map . we want to solve for .
- If we have an such that , then see that .So the kernel gives us our degrees of freedom: how much can we change around withoutchanging the solution.
- Now consider the cokernel: . If we want to find a solution . If we have , thenthe solution set is empty. The cokernel tells us the obstruction to a solution.