(a) Define kernel of a linear transformation. Prove that if U and V a…
Previous year question for Engineering Mathematics-III.
Question
(a) Define kernel of a linear transformation. Prove that if U and V are two vector spaces over the same field F, and $T : U \to V$ is a linear transformation, then kernel of T is a subspace of U.
(b) Find the matrix associated to the linear transformation $T : \mathbf{R}^3 \to \mathbf{R}^3$ defined by $T(x, y, z) = (9x + 4y + 5z, -4x - 3z, -6x - 4y - 2z)$ w.r.t the basis $B = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}$ of $\mathbf{R}^3$.
- Year: 2022
- Subject: Engineering Mathematics-III