Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
T : ℝn → ℝ such that T2 = λT for some λ ∈ ℝ Which of the following are true
1
\(\rm \|T(x)\|=|\lambda|\|x\| \forall x \in \mathbb{R}^n \)
2
if ||Tx|| = ||x for some nonzero x then |λ| = 1
3
T = λI
4
None of these