LT C16 (p443)

Find the matrix representation of:

\[\begin{align} T: C^{3} \xrightarrow[]{} C^{4}, T\left(\left[\begin{array}\\x\\y\\z\\\end{array}\right]\right) = \left[\begin{array}\\3x+2y+z\\x+y+z\\x-3y\\2x+3y+z\\\end{array}\right]\\ =x\left[\begin{array}\\3\\1\\1\\2\\\end{array}\right] + y\left[\begin{array}\\2\\1\\-3\\3\\\end{array}\right] + z\left[\begin{array}\\1\\1\\0\\1\\\end{array}\right]\\ = \left[\begin{array}\\ 3 & 2 & 1\\ 1 & 1 & 1\\ 1 & -3 & 0\\ 2 & 3 & 1\\\end{array}\right]\left[\begin{array}\\ x\\ y\\ z\\\end{array}\right] \end{align}\]