Linear Algebra - State the value of each unknown

[jinksys]

State the solution to each of the following systems. That is, clearly state the value of each of the unknown variables, x1, x2, x3, etc.

[0 1 0 1 0 -2
 0 0 1 -1 0 3
 0 0 0 0 1 -5
 0 0 0 0 0 0 ]

My attempt:

x2 = -2 -r
x3 = 3 - r
x4 = r
x5 = -5

This is apparently incorrect. My professor says x1 = s.

In the matrix x1 has the coefficient zero, how does x1 = s?

 

[Essnov]

In your solution, you have not assigned a parameter to x₁. Your solution is incomplete, basically. You just need to say x₁ is a free variable and state x₁ = s.

In other words, your solution is (x1, x2, x3, x4, x5) = (?, -2-r, 3-r, r, -5)

You're asked to state the value of each unknown, but you have not done so for x1. You have no information about x1 though, so all you can say is that it is a free variable. You assign an arbitrary parameter to it, x1 = s, and your solution becomes:

(x1, x2, x3, x4, x5) = (s, -2-r, 3-r, r, -5)

 

[jinksys]

In your solution, you have not assigned a parameter to x₁. Your solution is incomplete, basically. You just need to say x₁ is a free variable and state x₁ = s.

In other words, your solution is (x1, x2, x3, x4, x5) = (?, -2-r, 3-r, r, -5)

You're asked to state the value of each unknown, but you have not done so for x1. You have no information about x1 though, so all you can say is that it is a free variable. You assign an arbitrary parameter to it, x1 = s, and your solution becomes:

(x1, x2, x3, x4, x5) = (s, -2-r, 3-r, r, -5)

Thanks, now I understand.