Finding Unique solution for system of linear equations

[diggybob]

Hey guys, I am a little bit stuck on a recent math question and i was wondering if i could get some help about the best way to go about doing it

i have a matrice which is

1 2 -1 / -3
0 1 (-k-3) /-5
0 0 (k^2-2k) /(5k+11)

and i need to find when it has a unique solution, and infinitely many. Now i don't think i can have infinitely many because from what i understand the points at 3,3 and 3,4 both need to =0, and i can't find an x that does that. I am not sure how to go about finding the unique solution either.
i also can't get the matrix latex to work at all, sorry

 

[Prove It]

Hey guys, I am a little bit stuck on a recent math question and i was wondering if i could get some help about the best way to go about doing it

i have a matrice which is

1 2 -1 / -3
0 1 (-k-3) /-5
0 0 (k^2-2k) /(5k+11)

and i need to find when it has a unique solution, and infinitely many. Now i don't think i can have infinitely many because from what i understand the points at 3,3 and 3,4 both need to =0, and i can't find an x that does that. I am not sure how to go about finding the unique solution either.
i also can't get the matrix latex to work at all, sorry

First of all, the singular of "matrices" is "matrix", not "matrice".

You will have unique solution wherever the determinant nonzero.

Once you have the values of k where the determinant is 0, then you will need to substitute them into determine if you have repeated equations (which would mean infinite solutions) or parallel equations (which would mean no solutions)...