Exercise
https://texercises.com/exercise/linear-maps-and-matrices/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
For every linear Transformation T:K^nlongrightarrow K^mquad exists a matrix Ain M_mtimes nK s.t. TT_A.

Solution:
Proof. Define w_iTe_iquad forall leq ileq n. Since e_...e_n is a basis for K^n we know from the previous theorem. We know that every linear transformation S that satisfies Se_iw_iquad forall leq ileq n must coincide with T. Take Ain M_mtimes nK cols with w_...w_n. We have seen that T_Ae_iw_iquad forall leq ileq n Longrightarrow TT_A.
Meta Information
\(\LaTeX\)-Code
Exercise:
For every linear Transformation T:K^nlongrightarrow K^mquad exists a matrix Ain M_mtimes nK s.t. TT_A.

Solution:
Proof. Define w_iTe_iquad forall leq ileq n. Since e_...e_n is a basis for K^n we know from the previous theorem. We know that every linear transformation S that satisfies Se_iw_iquad forall leq ileq n must coincide with T. Take Ain M_mtimes nK cols with w_...w_n. We have seen that T_Ae_iw_iquad forall leq ileq n Longrightarrow TT_A.
Contained in these collections:

Attributes & Decorations
Tags
eth, hs22, linear map, lineare algebra, matrices, proof
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Creator rk
Decoration
File
Link