Help Me Solve Matrix: Show B†A† = C†

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Discussion Overview

The discussion revolves around a matrix problem involving the properties of matrix transposition and multiplication. Participants are trying to understand how to show that if the product C = AB is defined, then B†A† = C†, where A† and B† are the transposes of matrices A and B, respectively. The scope includes theoretical aspects of matrix operations and definitions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant requests help with the problem and expresses confusion about how to approach it.
  • Another participant asks for clarification on the definition of matrix B.
  • A participant suggests that since C = AB is defined, matrix B must be an n × c matrix, where c can be any number.
  • It is noted that A† is an n × m matrix, leading to the conclusion that B† is defined as a c × n matrix, thus making B†A† defined as a c × m matrix.
  • Another participant indicates that the second part of the problem follows from the first, suggesting that the multiplication of A† and B† will yield the desired result, but notes the need for definitions of each matrix.
  • A later reply expresses confusion about the previous explanations and requests further elaboration.

Areas of Agreement / Disagreement

Participants do not seem to reach a consensus on the clarity of the problem or the definitions of the matrices involved. There are multiple viewpoints regarding the definitions and implications of the matrix operations.

Contextual Notes

There are limitations in the discussion regarding the explicit definitions of matrices A and B, as well as the assumptions made about their dimensions and properties. Some mathematical steps remain unresolved, particularly in how the multiplication leads to the final equality.

theacerf1
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Please HELP! Matrix!

Please help me with the below question! I have no idea how to solve this, if someone could please help me with a solution and explain what they did and how they did it, it would be such a BIG help! Thanks! :)


If A is an m×n matrix with (i, j)-entry aij , let A† be the n×m matrix with (i, j)-entry
aji. Show that

(i) if the product C = AB is defined, then so is B†A†,
(ii) B†A† = C†.
 
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well can you define B ??
 


Thats all the question says, so confused :confused:
 


since C =AB is defined then the matrix AB is defined thus B is defined to be a n x c matrix where c is any number
since A† be the n×m matrix so B† is defined as a c x n so B† A† is defined as a c x m matrix therefore B† A† is defined
 


okay second part comes from the first part if C is AB then it is a m x c matrix use A† is an n x m matrix with (i, j)-entry aij mulitply with B† by saying that B is a c x n matrix with (i, j)-entry bij and mulitply them you will get your answer but one note i didnt give you details so you have to define each matrix
 


can anyone elaborate on this? i still don't get Elabed Haidar's answer. Sorry
 

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