Exam Post-mortem | Approximation Theory | May 2019

A1, A2 and A3 were bookwork type questions and were generally done well.

A4. A common mistake was to ignore the fact that $r$ might be zero. The
    P-F inequality is the key to showing uniqueness in this case.

A5. (Last part.) Most candidates knew that the matrix is nonsingular but
    did not provide a rigorous explanation (e.g. by showing that
    the quadratic form $x^T A x$ is positive for all nonzero vectors $x$.)  

A6  was another bookwork question and was generally done well.

A7  The first two parts were generally done well. Very few candidates got 
    the correct result $u_1=2/33$ in the final part.

B8. This tutorial sheet question was generally done well. Most attempts at
    part (c) were flawed. The connection between the $$L^2$ norm of the
    function $s_1$ and the quadratic form $x^T Q x$ was invariably missed.
    Some candidates forgot to show that $Q$ is tridiagonal when attempting
    part (d).
     
B9. A minority ofcandidates attempted this bookwork question. Those who made 
    a serious attempt got at least 14 marks. There were only a couple of 
    attempts to answer part (d).

B10. Most candidates who attempted this question got the first part correct.
     part (b) proved to be more problematic. Very few got more than 2 out of 
     5 marks for the final part. 

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