Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Let V be the real vector space of 2 x 2 matrices with entries in ℝ. Let T : V → V denote the linear transformation defined by T(B) = AB for all B ∈ V, where \(\rm A=\begin{pmatrix}2&0\\\ 0&1\end{pmatrix}\). What is the characteristic polynomial of T?
1
(x - 2)(x - 1)
2
x2 (x - 2)(x - 1)
3
(x - 2)2 (x - 1)2
4
(x2 - 2)(x2 - 1)