(a) Show that the mapping $T : \mathbf{R}^3 \to \mathbf{R}^2$ defined…
Previous year question for Engineering Mathematics-III.
Question
(a) Show that the mapping $T : \mathbf{R}^3 \to \mathbf{R}^2$ defined by $T(x, y, z) = (x - y, x + z), \forall (x, y, z) \in \mathbf{R}^3$ is a linear transformation.
(b) Find kernel, nullity, range and rank of the linear transformation $T : \mathbf{R}^2 \to \mathbf{R}^3$ defined by $T(x, y) = (x, x + y, y)$. Also verify rank-nullity theorem.
- Year: 2022
- Subject: Engineering Mathematics-III