Properties of Determinants for Lower Triangular Matrices?

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Homework Help Overview

The discussion revolves around the properties of determinants, particularly in the context of lower triangular matrices. The original poster is attempting to calculate the determinant of a 4x4 matrix by transforming it into a lower triangular form and multiplying the diagonal elements, but is encountering discrepancies with the expected answer.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster discusses the method of transforming a matrix into a lower triangular form and questions whether they are missing a property of determinants. Another participant points out the importance of the correct terminology regarding determinants. There is also a mention of row operations and their effects on the determinant value.

Discussion Status

The conversation is ongoing, with participants exploring the implications of different row operations on the determinant. Some guidance has been provided regarding which row operations affect the determinant, but there is no explicit consensus on the original poster's approach or the specific issue they are facing.

Contextual Notes

The original poster's attempts may be constrained by the need to adhere to specific rules regarding row operations and their effects on the determinant, which are under discussion.

cragar
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Homework Statement


I keep trying to turn a 4x4 matrix into a lower triangular matrix and then multiply along the diagonal to get the determinant , but I can't get the answer in the back of the book , is there some property about determinates I am missing .
 
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Hard to say without seeing your work.

BTW, the word is determinant.
 
ok as long as we add rows together it doesn't change the det(A)
i can go 5R1+R2=R2 and it won't change the det(A) correct.
 
Right. Of the three row operations, the only ones that change the value of the determinant are replacing a row by a multiple of itself (Rn <-- k*Rn) and switching two rows (Rn <--> Rm).
 

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