Solving the Inverse Matrix Problem: Constraints and Proof

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Homework Help Overview

The discussion revolves around determining the values of a variable \( t \) for which a given matrix \( A \) is invertible, as well as proving the non-existence of a specific type of 5x5 matrix. The subject area includes linear algebra, specifically focusing on matrix properties such as invertibility and determinants.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore conditions for matrix invertibility, particularly through the determinant. Questions about the implications of \( \text{det}(A) = 0 \) are raised, and there is a discussion about the initial steps needed to approach the problems presented.

Discussion Status

The discussion is ongoing, with participants questioning the conditions necessary for the matrix to be invertible and clarifying terminology related to determinants. There is no explicit consensus yet, but some guidance on focusing on the determinant has been suggested.

Contextual Notes

Participants express uncertainty about how to begin tackling the problems, indicating a need for foundational understanding of matrix properties. There is also a mention of potential confusion regarding the use of terminology in the context of determinants.

Naome666
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Homework Statement


Let a and b be fixed constants and t be a variable. For which values of t is the matrix
A = [1 1 1 ]
[a b t ]
[a^2 b^2 t^2 ] is invertible.

Also prove that there is no real 5x5 matrix such that (A^2)+I=0

Homework Equations





The Attempt at a Solution


 
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Interesting problem. Let me know when you've made some effort on it.
 
Naome666 said:

Homework Statement


Let a and b be fixed constants and t be a variable. For which values of t is the matrix
A = [1 1 1 ]
[a b t ]
[a^2 b^2 t^2 ] is invertible.

Also prove that there is no real 5x5 matrix such that (A^2)+I=0

I don't even know where to begin this two problems!
 
Well, what are some conditions for a matrix to be invertible?
 
aPhilosopher said:
Well, what are some conditions for a matrix to be invertible?

Determine (A) = 0
 
Cool (although you have it backwards). What conditions on t make Det(A) = 0?
 
determinant(A) not equal to 0. "Determine" is a verb.
 

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