rank and nullity of of Linear Transformation BHU PET 2020 Mathematics cmi tifr gate cmi hcu tgt pgt

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Linear Algebra: Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions, eigenvalues, and eigenvectors for matrices, Cayley-Hamilton theorem.
orthogonal matrices.
9. Let V=M_(2×2) (R) be a vector space and M=(■(1&2@0&3)).Let T∶V→V be a linear map such that
T(A)=AM- MA. Then the rank of T is
(a) 3 (b) 4 (c) 2 (d) 1
En BHU PET 2020, 9
Key