A question in understanding a mistake

  • Thread starter Thread starter transgalactic
  • Start date Start date
  • Tags Tags
    Mistake
Click For Summary
SUMMARY

The discussion revolves around a mathematical problem involving an operator with parameters related to a matrix. The user seeks clarification on finding the values of parameters a, b, and c that maximize the dimensions of the kernel and image of the operator. The confusion arises from a perceived mistake made by the teacher in both the kernel and image calculations, specifically regarding the use of a zero equation for the kernel and the transposition of the matrix for the image. The user requests validation of their interpretation of the problem.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically kernel and image of linear operators.
  • Familiarity with matrix transposition and its implications on vector independence.
  • Knowledge of parameter optimization techniques in mathematical contexts.
  • Ability to interpret and analyze mathematical equations and their solutions.
NEXT STEPS
  • Study the properties of linear transformations and their kernels.
  • Learn about matrix transposition and its effects on vector spaces.
  • Explore optimization techniques for parameterized equations in linear algebra.
  • Investigate common mistakes in teaching linear algebra concepts and how to address them.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on linear algebra, as well as anyone involved in teaching or learning about matrix operations and their applications.

transgalactic
Messages
1,386
Reaction score
0
http://img88.imageshack.us/my.php?image=img86311lj7.jpg
(traverse is a typing mistake i ment transpose)

i am given an operator with parameters (the original matrix)
and i was told to find
for which values of a b c
we have the maximal dim ker t
and the the maximal dim I am t

the person who solved it ,
in the ker part he makes an equation with 0

and in the I am part he transposes the matrix and looks for what value of the parameters
we have the maximal amount of independent vectors

so why the teacher written a mistake in both parts??
 
Last edited:
Physics news on Phys.org
can you tell me if you agree with me
or you don't understand the question
i'll refrase it
if needed
 

Similar threads

Linear Algebra - Kernel and range of T
  • · Replies 5 ·
Replies
5
Views
2K
Exercise with Linear Transformation
  • · Replies 13 ·
Replies
13
Views
2K
Linear Transformation and Isomorphism
  • · Replies 10 ·
Replies
10
Views
2K
Graduate How Does the Non-Equality of Kernels Imply Their Sum Equals the Vector Space?
  • · Replies 2 ·
Replies
2
Views
2K
Why is this method valid to show function is PSD?
  • · Replies 3 ·
Replies
3
Views
2K
Want to understand proof of Dimension/ Rank-Nullity theorem
  • · Replies 2 ·
Replies
2
Views
4K
Solving a system of differential equations by fundamental matrix
  • · Replies 8 ·
Replies
8
Views
3K
Linear algebra - Image and Kernel
  • · Replies 4 ·
Replies
4
Views
3K
Finding the Jordan canonical form of a matrix
  • · Replies 7 ·
Replies
7
Views
4K
Linear Transformations if the design matrix
  • · Replies 8 ·
Replies
8
Views
2K