# Due on Feb 20

1. For a square matrix $$A$$, prove that $$(A^{-1})^\top = (A^\top)^{-1}$$. (5 points)

2. Find the gradient of $$f(A)=X^\top A X$$ with respect to $$A$$, where $$X$$ is a column vector and $$A$$ is a matrix. Note that $$A$$ is the variable here, rather than $$X$$ as discussed in class. (5 points)

3. Try to build a linear regression model to predict the stock price of MSFT from the prices of several other stocks. You can download the Jupyter notebook of the question from here. (10 points)