Answer
$A$ is an invertible matrix.
(Th.8, (a) and (b))
Work Step by Step
(The exercise wants us to use technology)
Defining A in MATLAB (or, in my case a clone: OCTAVE GNU)
A=[5 3 1 7 9; 6 4 2 8 -8; 7 5 3 10 9; 9 6 4 -9 -5; 8 5 2 11 4]
rref(A}
returns the $I_{5}$ matrix,
$\mathrm{b}. \quad A$ is row equivalent to the $n\times n$ identity matrix.
is valid. Then, by Th.8
$\mathrm{a}. \quad A$ is an invertible matrix.
is valid as well
$A$ is an invertible matrix.
(Th.8, (a) and (b))
