- If the columns of a 7x7 matrix D are
linearly independent, what can be said about the solutions D
*x*=*b* for a given
7x1 *b* (where *x* is 7x1 too)?

a) D*x*=*b* has at least one solution, but we cannot say anything
more about the solution or solutions

b) D*x*=*b* has a unique solution, but we cannot say anything more about it

c) D*x*=*b* has a unique solution, and I can tell you what it is

d) D*x*=*b* has infinite solutions

e) D*x*=*b* has no solutions for some *b* and infinite solutions for other *b*

- If the columns of a 7x6 matrix D are
linearly independent, what can be said about the solutions D
*x*=*b* for a given *b*,
with *x* as 6x1 and *b* as 7x1?

a) D*x*=*b* has at least one solution, but we cannot say anything
more about the solution or solutions

b) D*x*=*b* always has a unique solution

c) D*x*=*b* has no solutions for some *b* and infinite solutions for other *b*

d) D*x*=*b* has one solution for some *b* and no solutions
for other *b*

e) We can only reason that D*x*=*b* has 0, 1 or infinite solutions as
with any linear system.

1. c)
2. d)