In a 3-dimensional coordinate system, draw the column vectors of matrix A, the column vector space of A, b, ˆb, and b′. Make sure that the drawing is reasonably accurate which can reflect the relationship among these quantities.
a) Draw the column vectors of matrix A as arrows in 3D space with appropriate coordinates
b) Represent the column vector space of A as a 3D plane that contains all possible linear combinations of the column vectors of A
c) Draw the vector b as an arrow in the 3D space
d) Show the vectors ˆb and b′ as projections of b onto the column vector space of A, with their tails starting at the tip of b