5. Determine whether the given linear transformation is invertible. If it is, then find the
formula for its inverse.
\begin{align*}
(a) \ T: \mathbb{R}^2 \to \mathbb{R}^2, \text{ given by } T\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} x+2y \\ 5x+7y \end{pmatrix}; \\
(b) \ T: \mathbb{R}^3 \to \mathbb{R}^3, \text{ given by } T\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} x+2y+z \\ -3x+y-2z \\ 4x-6y+2z \end{pmatrix}; \\
(c) \ T: \mathbb{R}^3 \to \mathbb{R}^3, \text{ given by } T\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} x+z \\ -3x+y-2z \\ 2x-y \end{pmatrix}.
\end{align*}
