Finding the inverse of this matrix.

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    Inverse Matrix
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Homework Help Overview

The discussion revolves around finding the inverse of a matrix, specifically involving expressions that include a vector of ones and matrix multiplication. Participants are exploring the properties of these matrices and their products.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of multiplying matrices to demonstrate the identity matrix. There is uncertainty about whether to write the matrices in standard form or work with them in their current expressions. Some participants suggest that the expressions represent matrices of ones and raise questions about the dimensions and properties of these matrices.

Discussion Status

There is ongoing exploration of the problem, with participants providing tips and clarifications regarding the nature of the matrices involved. Some guidance has been offered about the multiplication of the matrices and the implications of the dimensions, but no consensus has been reached on the approach to take.

Contextual Notes

Participants are considering the implications of the notation used, particularly regarding the vector of ones and its dimensions. There is a mention of potential confusion arising from the notation and the need for clarity on whether the vector is a column vector.

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Homework Statement



Hi there I'm trying to solve this question:

dPs5M.png


Homework Equations





The Attempt at a Solution



I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I should write them out in matrix form first or just do them as is?
 
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Kuma said:

Homework Statement



Hi there I'm trying to solve this question:

dPs5M.png


Homework Equations





The Attempt at a Solution



I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I should write them out in matrix form first or just do them as is?
I haven't worked this all the way through, but your idea of multiplying the two expressions seems like the way to go.

Here are a couple of tips that might be helpful. The 1n1n' expressions represent n x n matrices whose entries are all 1's.

The product 1n1n' * 1n1n' works out to be n * 1n1n', which you might need to prove by induction.
 
It says that 1n is a vector of 1's so shouldn't 11' = n?
 
Kuma said:
It says that 1n is a vector of 1's so shouldn't 11' = n?

They probably mean that 1_n is a column vector. Otherwise the dimensions wouldn't agree. Indeed: (1-\rho)I would be a matrix and 1_n1_n^\prime would be a number, so you can't add them.
 
I agree with micromass. 1n has to be a column vector.
 

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