Compute Determinant of Matrix A: max(i,j)

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Homework Help Overview

The problem involves computing the determinant of an n × n matrix A defined by the elements aij = max(i, j). The original poster seeks clarification on the meaning of this matrix definition.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the interpretation of the matrix elements, with some providing examples and clarifications about the behavior of the max function in different positions of the matrix.

Discussion Status

The discussion has provided clarifications regarding the definition of the matrix elements. A hint has been offered about the relationship between the indices i and j in different regions of the matrix. The original poster's question appears to have been addressed, but further exploration may be needed if additional questions arise.

Contextual Notes

Participants have noted that this is a homework thread and have requested that no further assistance be given unless the original poster asks additional questions.

iasc
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The question is:
Compute the determinant of the n × n matrix A for which aij = max(i, j).

I can compute determinants but I don't really know what the last bit means.
Any help appreciated.
 
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iasc said:
The question is:
Compute the determinant of the n × n matrix A for which aij = max(i, j).

I can compute determinants but I don't really know what the last bit means.
Any help appreciated.

Put some numbers in. For example, a12 = max(1, 2) = 2.
 
max(i,j) means either i or j, whichever is greater.
 
Huge hint:
In the main diagonal of your matrix i = j, so max{ i, j } = i or j
above the main diagonal j > i, so max{ i, j } = j
below the main diagonal i > j so max { i, j } = i
 
Note to all:

The OP had a simple question about the meaning of

aij = max(i, j)​

The question has been answered. This is a homework thread; please do not provide further help on solving the problem unless the OP posts again with more questions.
 

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