1
answer
0
watching
175
views
10 Nov 2019
Give an example of a 3 times 3-matrix A such that A^2 notequalto 0 but A^3 = 0. (b) Let n N, and suppose that T: R^n rightarrow R^n is a linear transformation such that T^n-1 notequalto 0 but T^n = 0. Show that there exists upsilon R^n such that (upsilon, T upsilon, ..., T^n-1 upsilon) is a basis or R^n. (c) A square matrix B is called nilpotent if B^m = 0 for some m N. Prove that if B is a nilpotent n times n matrix, then B^n = 0.
Give an example of a 3 times 3-matrix A such that A^2 notequalto 0 but A^3 = 0. (b) Let n N, and suppose that T: R^n rightarrow R^n is a linear transformation such that T^n-1 notequalto 0 but T^n = 0. Show that there exists upsilon R^n such that (upsilon, T upsilon, ..., T^n-1 upsilon) is a basis or R^n. (c) A square matrix B is called nilpotent if B^m = 0 for some m N. Prove that if B is a nilpotent n times n matrix, then B^n = 0.
Nelly StrackeLv2
21 Jul 2019