Misconceptions Of Linear Algebra 2008 Paper
1.
Many students did not normalise the orthogonal vectors. I don’t
understand this because they have carried out all the hard work in finding the
orthogonal vectors and then they fail to normalise these. To normalise nonzero vectors divide by the norm of the vector.
2.
Students in general avoid doing proof questions. This is a serious issue
omission on a pure mathematics paper.
3.
It is amazing how many times students fail to read the question. The
question asked the students to find the eigenvalues and eigenvectors but many
did not find the eigenvectors.
4.
Some students wrote the eigenvector as the zero vector. How many
times have they been told that the eigenvector cannot be the zero vector.
5.
For the norm f many students evaluated f
the square root.
6.
Some students wrote w 
2
2
and then did not take
w, w . This is wrong because
w  w, w
2
7.
To show a result concerning u  v  many students assumed that
the given vectors u and v were orthogonal, that is their inner product is zero,
u, v  0 .
2