Working on this problem. Actually 2 problems, involving Gaussian elimination. Both of them say
Find the values of such that the system has (a) a unique solution (b) no solution and (c) infinitely many solutions
I am required to use Gaussian Elimination
The first problem is
My solution is as follows, but not sure if correct (not sure how to do latex for this). I have seperated each entry by a comma (,)
row 1 = 1, k, -1
row 2 = k, 1, 1
-k * R1 + R2 = 0, -(k2)+1, k+1
(a) if k = -1 R3 = 0, 0 and has infinitely many solutions
(b) if k = 1 R3 = 0, 2 and is inconsistant
(c) if k != 1 and k != -1 the system has a unique solution
I'm not sure if that is correct. I've gone through the problem several times, and come up with the same outcome everytime, but I'm new to this. I did really well at basic Matrix stuff, but this is the next paper after the intro one.
The second problem is
I've gone through this a whole lot of times (I need to use Gaussian elimination) and end up with some unfactorable equation at the end. Where should I start with this problem? I don't want the answer, just some help.
What I have been doing is laying it out in a compact matrix and then multiplying the rows to eliminate the x and y values.
Here is my working - not sure if it is correct.