the question is on Section 1.4 exercise 7, it says:
find all solutions of
$$2x_1 - 3x_2 - 7x_3 + 5x_4 + 2x_5 = -2$$
$$x_1 - 2x_2 - 4x_3 + 3x_4 + x_5 = -2$$
$$2x_1 - 4x_3 + 2x_4 + x_5 = 3$$
$$x_1 - 5x_2 - 7x_3 + 6x_4 + 2x_5 = -7$$
My answer seems to be that there is no solution, could I ask for a confirmation of this result?
That is not correct there is in fact a solution.
The associated matrix is
Which can be row reduced to
This is absolutely valid for a solution. Moreover there are infinitely many solutions.