1. Which of the following are true about M:=Matrix([[1,4],[2,5],[3,6]])? Note that when M is augmented with a generic vector and reduced to Gaussian, the last row becomes [0 0 b₁-2b₂+b₃]
   a) The column space is the plane b₁-2b₂+b₃=0 in R³
   b) The column space is the plane sVector([1,2,3]) + tVector([4,5,6]) in R³
   c) The nullspace is the 0 vector in R²
   d) more than one of the above, but not all of them
   e) all of a), b), c)
   
   
   
   
2. If an matrix is not square, then
   a) the column space is a subspace of R^{number of rows}
   b) the column space is a subspace of R^{number of columns}
   c) further work must be done to tell.
   
   
   
   
3. The definition of a basis is a linearly independent spanning set for V. Which of the following also describes a basis?
   a) A basis is a minimal spanning set for V.
   b) A basis is a largest possible set of linearly independent vectors in V.
   c) An efficient way (linearly independent) to represent a space (span) linearly.
   d) all of the above
   e) two from a), b), c) but not all three
   
   
   
   Solutions
   1. e)
   2. a)
   3. d)