Question

say I'm given the following matrix that represents a linear system

{1,2,1|1
-1,4,3|2
2,-2,x|3}

What values of x would make the system have a unique solution? The answer is x =/= -2, but I honestly have no idea how to even approach this problem. Any hints?

Answer 1

Try doing Gauss-Jordan Elimination on the first 2 columns.

Answer 2

did you by chance mean rows? doing rref on the first two columns gibes me an "invalid dim" error on the calculator. although doing G-J elimination on the first two rows gives me a row-echelon matrix where i dont know where to proceed either...thanks for the response!

Answer 3

1, 2, 1|1 r1
-1, 4, 3|2 r2
2, -2, x|3 r3


r1-r2

2,-2,-2|-1

Answer 4

notice that if x=-2 then 3 would have to equal -1 , which can never happen

Answer 5

thanks!