Solving Matrices with Standard Base Formula for Ker (T)

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SUMMARY

The discussion focuses on finding the kernel (ker) of matrices using the standard base formula. The user encountered an issue where their calculations consistently resulted in the zero vector, which did not match the expected answer from the textbook. The user applied the equation A*(x,y,z)=(0,0,0) but struggled with the simplification process. The key takeaway is the importance of correctly simplifying the matrix to accurately determine the kernel.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically kernel and image of a linear transformation.
  • Familiarity with matrix operations and simplification techniques.
  • Knowledge of standard basis vectors in vector spaces.
  • Proficiency in solving systems of linear equations.
NEXT STEPS
  • Study the process of finding the kernel of a linear transformation in detail.
  • Learn about row reduction techniques for simplifying matrices.
  • Explore examples of kernel calculations in linear algebra textbooks.
  • Investigate the relationship between the kernel and the rank-nullity theorem.
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Students and educators in linear algebra, mathematicians focusing on vector spaces, and anyone seeking to deepen their understanding of linear transformations and their properties.

transgalactic
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i am given a formula and asked to find the ker
of the matrices of the standart base

this is the link were i tried to solve it:

http://img297.imageshack.us/my.php?image=img7979ds0.jpg

when i try to find the ker (T)

i get all zeros

i don't know where i get it wrong

my theory says that after we simplify the matrix
A*(x,y,z)=(0,0,0)

so i built equation and all i get is all zeros
and that not the answer in the book
where did i got it wrong?
 
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how to find ker (t) ??
 

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