(b) Suppose farmer 2 cannot be served by reservoir 3 because the farmer is at a higher altitude than the
the reservoir. How can you take this into account in your model without increasing the number of constraints
Optional linear algebra review
This problem will not be graded but you will receive feedback if sub-
(d) Prove that if
are 3-dimensional subspaces of
must have a nonzero vector
in common. HINT: Start with bases for the two subspaces, making six vectors in all. Consider notions
of linear independence.
True or False:
(i) If the columns of a matrix
are linearly independent, then
has exactly one
solution for every
. (ii) A 5 by 7 matrix never has linearly independent columns.