1. If the columns of a 7x7 matrix D are linearly independent, what can be said about the solutions Dx=b for a given 7x1 b (where x is 7x1 too)?
a) Dx=b has at least one solution, but we cannot say anything more about the solution or solutions
b) Dx=b has a unique solution, but we cannot say anything more about it
c) Dx=b has a unique solution, and I can tell you what it is
d) Dx=b has infinite solutions
e) Dx=b has no solutions for some b and infinite solutions for other b

2. If the columns of a 7x6 matrix D are linearly independent, what can be said about the solutions Dx=b for a given b, with x as 6x1 and b as 7x1?
a) Dx=b has at least one solution, but we cannot say anything more about the solution or solutions
b) Dx=b always has a unique solution
c) Dx=b has no solutions for some b and infinite solutions for other b
d) Dx=b has one solution for some b and no solutions for other b
e) We can only reason that Dx=b has 0, 1 or infinite solutions as with any linear system.

1. c) 2. d)