Let T: \(\mathbb{R}^3 \to \mathbb{R}^3\) be a linear transformation such that \(T(1, 0, 0) = (-1, 4, 2)\), \(T(0, 1, 0) = (3, 1, -2)\), and \(T(0, 0, 1) = (0, 2, -2)\). Find the indicated image.
\(T(1, 0, -3)\)
\(T(1, 0, -3) = \)
Let T be a linear transformation from \(\mathbb{R}^2\) into \(\mathbb{R}^2\) such that \(T(1, 0) = (1, 1)\) and \(T(0, 1) = (-1, 1)\). Find \(T(1, 4)\) and \(T(-3, 1)\).
\(T(1, 4) = \)
\(T(-3, 1) = \)