Consider $$A = \begin{bmatrix}&8 & 2 & -2 & 0 &5 \\&12 & 3 &…
Consider $$A = \begin{bmatrix}&8 & 2 & -2 & 0 &5 \\&12 & 3 & -3 & 6 &0 \\&4 & 1 & -1 & 3 &5 \\&0 & 0 & 0 & 1 &5\\&6 & \frac{3}{2} & -\frac{3}{2} & 3 & 0 \end{bmatrix}$$ a) Find the nullspace of A (Nul(A) = span\{…\}). b) Find a basis for the column space of A. c) Is A invertible? Justify your answer using 3 different reasons using the Invertible Matrix Theorem.