Notations: ■Rmxn: the set of m x n matrices with entries in R.■ : the transpose (inverse) of matrix

問題詳情

Notations:

■Rmxn: the set of m x n matrices with entries in R.

■

: the transpose (inverse) of matrix A.

■ det
(A): the determinant of matrix A.

■ Null
(A): the null space of matrix A.

■ rank
(A) (nullity
(A)): the rank (nullity) of matrix A.

■ In: the identity matrix of size n x n.

■

: the matrix representation of T relative to a and β.

(1) True or False (If true, prove it; if false, give a counterexample or disprove it).
【題組】(i) (3%) For any

, det(2.A) = 2 det
(A).