N times opeparations(lenear algebra)

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Homework Help Overview

The discussion revolves around calculating the determinant of a matrix that involves a variable "n" and solving related equations. The subject area is linear algebra, specifically focusing on determinants and polynomial equations derived from them.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss methods for calculating the determinant of a matrix with variable dimensions. There are attempts to apply Cramer's law and to analyze the determinant for specific values of n. Questions arise regarding the nature of the equations and the implications of the variable n.

Discussion Status

Some participants have provided insights into the nature of the determinant as an nth degree polynomial equation and have explored specific cases to identify patterns. There is acknowledgment of a correct approach to solving the determinant, although there is no explicit consensus on all aspects of the problem.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available and the methods they can use. The discussion includes assumptions about the properties of determinants and the structure of the matrix involved.

transgalactic
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how to calculate the determinant of this:
http://img6.imageshack.us/img6/4937/16190333pz1.gif

b)
solve this
http://img88.imageshack.us/img88/4556/73223491zz9.th.gif

if it were a defined matrix i could sol it
but there its "n" times

??
 
Last edited by a moderator:
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i solved A
how to solve B??
i think of using cramer law
but its an endless equation
??
 
No, it's not an "endless" equation. For a given n, this is an n+1 by n+1 determinant equal to 0 so it is an nth degree polynomial equation.

Have you tried it for n= 1, n= 2, etc.? You should be able to see a pattern pretty quickly. The roots are 0, 1, 2, ..., n-2.

In fact it should be easy to see that if x= 0, the first two rows are exactly the same so the determinant is 0. If x= 1, the first and third rows are exactly the same. If x= 2, the first and fourth rows are exactly the same, etc.
 
Last edited by a moderator:
ok if i subtract the first row from the rest i get a diagonolized matrix
|1 1 1 .. 1|
|0 -x . . .. 1|
|0 0 1-x 1|
|0 0 0 .. n-2-x|

-x(x-1)(x-2)...((n-2)-x)=0
so the roots are from x=0 to x=n-2
that correct??
 
Yes, that is correct and a good way to solve it. (You shouldn't have the "1"s above the diagonal though.)
 

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