Tutor profile: Onyebuchi E.

Create a list that contains the squares of all numbers from 1 to 100 which are divisible by 2 or 3.

squares = [v**2 for v in range(1,101) if v % 2 == 0 or v% 3 == 0]

Prove that if a matrix $$A$$ is one-to-one then the nullspace of $$A$$ is $$\{0\}$$.

Suppose the contrary is true so that there exists non-zero vector $$\mathbf{u}$$ in the nullspace of $$A$$. Then we know that $$A\mathbf{u}=0 = A\mathbf{0}$$ but $$\mathbf{u} \neq \mathbf{0}$$. This would imply that $$A$$ is not one-to-one. Therefore, if $$A$$ is one-to-one it must be the case that the nullsapce of $$A$$ is $$\{0\}$$.

What is "overfitting"? Describe something that could potentially cause overfitting?

Overfitting occurs when a model is tuned to predict a set of data too closely, and thus fails to properly generalize to new data. One thing that could potentially cause overfitting is overparameterization. For instance, if we had a set of $$n$$ points in $$\mathbb{R}^2$$ that we interpolated with a polynomial of degree $$n-1$$ we could precisely hit the correct values for these points. However, the resulting curve would fluctuate wildly and likely be very inaccurate for new data points.