Grading comments: 

Q1
very few students proved the result directly. (3/3)
many students used the result QQ^T = I which leads to circular logic. (2/3)

Q2a 
one point each for
- 2nd order
- first dervative
- sqrt(x)

Q2b
one point each

Q2c
most points lost were from algebra mistakes (or not knowing to multiply with the conjugate)

Q2d
2 for limit, 1 for how it relates to f

Q3a
no comments

Q3b
many students did not give rho (3/5). 

Q3c
no comments

Q4a
some students used a positivity argument (A is positive, therefore x^TAx is positive). This was accepted with full credit. 

Q4b
Many students used frobenius norm. Unspecified matrix norms should be the 2,2 operator norm, and this was clarified in class after multiple students asking. 

Q4c
- 1 for def. of cond num
- 1 for correct expression/numerical value

Q4d
- many students described how to get the cholesky decomposition, which was not necessary. 

Q5 
nobody saw that the matrix A was rank-deficient, which necessiated the use of SVD (3/3).
    alternatively, rank-revealing QR can also work, but we didn't cover that.  
many students formed the normal equations (2/3)
some students tried to drop equations or use LU (0/3)

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Question averages: 

4b  0.54 / 2 (27.03%)
5   1.09 / 3 (36.49%)
4d  1.54 / 4 (38.51%)
3a  1.18 / 3 (39.19%)
1   1.43 / 3 (47.75%)
4c  0.99 / 2 (49.32%)
2d  1.61 / 3 (53.60%)
2a  1.69 / 3 (56.31%)
2b  1.23 / 2 (61.49%)
2c  3.27 / 5 (65.41%)
3b  3.38 / 5 (67.57%)
4a  2.92 / 4 (72.97%)
3c  2.32 / 3 (77.48%)