Exercise
https://texercises.com/exercise/determinant-function-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:
forall ngeq exists at least one determinant function M_ntimes nKlongrightarrow K.

Solution:
Proof. Induction on n. For n M_times Klongrightarrow K amapsto a is a determinant function. For n we have seen that a determinant function. M_times Klongrightarrow K exists. If a determinant function exists for M_n-times n-K then by the previous theorem a determinant function exists also for M_ntimes nK.
Meta Information
\(\LaTeX\)-Code
Exercise:
forall ngeq exists at least one determinant function M_ntimes nKlongrightarrow K.

Solution:
Proof. Induction on n. For n M_times Klongrightarrow K amapsto a is a determinant function. For n we have seen that a determinant function. M_times Klongrightarrow K exists. If a determinant function exists for M_n-times n-K then by the previous theorem a determinant function exists also for M_ntimes nK.
Contained in these collections:

Attributes & Decorations
Tags
determinant, eth, fs23, lineare algebra, matrices, proof
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Creator rk
Decoration
File
Link