Thread: For what value of k.. no solution / unique solution / infinitely many solutions

The question is really confusing me, I have no clue what its asking/how to do it. What I do know..

a) No solution occurs when the bottom row is all zeroes except for the constant. Like (0 0 0 4) because 0 = 4 is impossible.

b) A unique solution occurs when the leading 1s are in a perfect diagonal like:

(1 0 0 0)
(0 1 0 0)
(0 0 1 0)

c) And infinitely many solutions for anything else.


How would I go about doing this im completely confused

Whoa there! Please do not define these concepts in terms of the mechanical outcomes. Concentrate on the concepts of dependence vs independence and consistent vs inconsistent.

Have you met the Determinant? It will help, here.

An obvious observation is k = 1. What does that do to the three equations?

k = -2 is a little less obvious, but equally interesting.