Can you prove E_{ij}AE_{kl}=a_{jk}E_{il} with the given formula for A?

Thread starter lesliemath
Start date Sep 24, 2011
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Matrix

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SUMMARY

The discussion centers on proving the equation E_{ij}AE_{kl}=a_{jk}E_{il} using a specific formula for matrix A. Participants emphasize the importance of substituting the provided formula for A into the equation and manipulating the indices accordingly. The key steps involve understanding the properties of matrix multiplication and the role of the elementary matrices E_{ij} and E_{kl}. This proof is essential for grasping advanced concepts in linear algebra and matrix theory.

PREREQUISITES

Understanding of matrix multiplication and properties
Familiarity with elementary matrices, specifically E_{ij} and E_{kl}
Knowledge of matrix notation and indexing conventions
Basic concepts of linear algebra, including matrix transformations

NEXT STEPS

Study the properties of elementary matrices and their applications in linear algebra
Learn about matrix multiplication rules and index manipulation techniques
Explore advanced topics in linear algebra, such as eigenvalues and eigenvectors
Review proofs involving matrix identities and transformations

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Students and educators in mathematics, particularly those focusing on linear algebra, matrix theory, and proof techniques. This discussion is beneficial for anyone looking to deepen their understanding of matrix operations and properties.

Sep 24, 2011

lesliemath

matrix -- proving need help!

please help i have no idea how to do this question. please give me some hints :(

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Sep 24, 2011

Fredrik

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Part (a) is asking you to show that E_{ij}AE_{kl}=a_{jk}E_{il}, and it's giving you a formula for A. So why don't you start by writing E_{ij}AE_{kl}=, and then use the formula for A that you were given?

Last edited: Sep 24, 2011