Im really stuck on this question (well, a series of questions that are all related to finding existence of solutions and just want to know how to do one so I can do the rest).
Determine the values of k for which the system of linear equations has i). no solution vector, ii). a unique solution vector, iii). more than one solution vector (x,y, z).
kx + y + z = 1
x + ky + z = 1
x + y + kz = 1
I've made up a matrix with all these coeffiecients in it but after performing row operations on it, for the last row in the matrix, I get:
2-k^2 - k = 1-k
Which after you rearrange it its k^2 = 1
But the solution says (for the no solution vector one): k =-2 no solution and I have no idea how they got it.
for the unique solutions, it says k is all real numbers except for -2 and 1 (with some values in a matrix).
And for the multiple solutions, it says k = 1 (with some values in a matrix).
I really really really really need help. This question is driving me insane
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