How would you solve a matrix with constants inside of it (such as h,k). An example I was given was
-7x + 3y + 4z = 3
-4x - 4y - 4z = -5
29x -y + h = k
and was told to find "This system has a unique solution whenever "
What I did was bring the matrix to a form as close as I could to row echelon form, but I have no idea what the conditions are to find what k isnt equal to for a unique solution to be found.
The near row echelon form I found was
x + 11y + 12z = 13
0x + 1y + 11/10z = 47/40
0x + 0y + (9/5 + h)z = k + 67/20
and from there I'm at a complete loss as to how to solve the problem
Edit: It'd also be appreciated if someone could let me know the conditions for a similar problem, but with infinite solutions and with no solutions
Edit 2: The question was actually when , not k, sorry for the inconvenience!