Construct a 2x2 matrix that is not the zero vector

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Discussion Overview

The discussion revolves around the construction of a 2x2 matrix that is not the zero vector while satisfying the condition that its square equals zero (A^2 = 0). The scope includes mathematical reasoning and exploratory approaches to the problem.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant seeks assistance in constructing a 2x2 matrix that meets the specified criteria.
  • Another participant clarifies the question, confirming the requirement for the matrix to be non-zero while satisfying A^2 = 0.
  • Suggestions are made to approach the problem geometrically, through basis vectors, or by explicitly writing out a general matrix and determining the conditions for its square to be zero.
  • A participant mentions the concept of nilpotence as an interesting but not directly helpful related topic.
  • Another suggestion involves explicitly writing out the matrix and squaring it to derive the necessary equations for the result to be the zero vector.

Areas of Agreement / Disagreement

Participants generally agree on the requirements for the matrix and propose various methods to explore the problem. However, there is no consensus on a specific solution or approach to take.

Contextual Notes

Participants have not resolved the mathematical steps necessary to find the matrix, and the discussion includes various assumptions about the methods of approach.

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Construct a 2x2 matrix that is not the zero vector yet satisfies A^2=0 been studying this question for a while...any help?
 
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Do you mean A is a 2x2 matrix which is not a zero matrix, and it is such that A^2 = 0 ?
 
a) think geometrically

OR

b) think in terms of basis vectors

OR

c) just do it - write out a general a,b,c,d matrix square it and see what choices of a,b,c,d would mean its square is 0.
 
Look up nilpotence too, won't help you solve the question but its interesting and related to it :)
 
Or even, just write out a matrix

[a b]
[c d], square it and see what equations must be satisfied to be the 0 vector!
 

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