N times opeparations(lenear algebra)

  • Thread starter transgalactic
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In summary, the conversation discusses how to calculate the determinant of a given matrix and solve a defined matrix. The conversation also explores the use of Cramer's law and finding patterns in the matrix to solve for the roots. Ultimately, it is determined that the roots are from x=0 to x=n-2.
  • #1
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

??
 
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  • #2
i solved A
how to solve B??
i think of using cramer law
but its an endless equation
??
 
  • #3
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.
 
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  • #4
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??
 
  • #5
Yes, that is correct and a good way to solve it. (You shouldn't have the "1"s above the diagonal though.)
 

Related to N times opeparations(lenear algebra)

1. What is N times operations in linear algebra?

N times operations in linear algebra refer to the number of times a mathematical operation is performed on a set of N elements or vectors. This is commonly used in matrix operations, where a matrix with N rows and columns is multiplied by another matrix with N rows and N columns.

2. What are the different types of N times operations in linear algebra?

There are three main types of N times operations in linear algebra: addition, subtraction, and multiplication. Addition and subtraction involve adding or subtracting corresponding elements in two matrices with the same dimensions. Multiplication involves multiplying corresponding elements in two matrices and summing the results.

3. How do N times operations differ from regular operations in linear algebra?

N times operations differ from regular operations in linear algebra in that they involve performing the same operation on multiple elements of a matrix instead of just two elements. This allows for more complex calculations and transformations of data.

4. Why are N times operations important in linear algebra?

N times operations are important in linear algebra because they allow for efficient calculations and transformations of data. They are also essential in solving systems of linear equations and performing other higher-level mathematical operations.

5. Can N times operations be performed on matrices with different dimensions?

No, N times operations can only be performed on matrices with the same dimensions. This is because the corresponding elements in two matrices with different dimensions cannot be multiplied or added together. However, matrices with different dimensions can be transformed to have the same dimensions before performing N times operations.

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