Problem 44531. 2) Are you more familiar with iteration methods or Linear Algebra ? Let's see together.

Created by Riccardo Dessì

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Referring to problem:https://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-togetherGiven a sum result x value of a N number of addends, build an array of N elements y such that the following equality is satisfied: sum(y) = x .For example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].More formally if x = a and N = n it results:y = [y_1 y_2 y_3 ... y_n]
where: y_1 + y_2 + y_3 +...+ y_n = aImportant notice: All the elements in y must be: different from zero, different from each other and strictly positive . On the other hand I will not take into account if they are integers or decimal numbers .Hint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.Good luck and enjoy with the solution ;)

Referring to problem:

https://www.mathworks.com/matlabcentral/cody/problems/44530-are-you-more-familiar-with-iteration-methods-or-linear-algebra-let-s-see-together

Given a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .

For example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].

More formally if x = a and N = n it results:

y = [y_1 y_2 y_3 ... y_n]
where:  y_1 + y_2 + y_3 +...+ y_n = a

Important notice: All the elements in y must be: *different from zero*, *different from each other* and *strictly positive* . On the other hand I will not take into account if they are _integers or decimal numbers_ .

Hint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.

Good luck and enjoy with the solution ;)

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Last Solution submitted on Feb 21, 2023

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Jiahang Li on 24 Feb 2018

There is a unique solution to the linear equations.

Riccardo Dessì on 24 Feb 2018

Dear Jia, the solution is not unique. I've upload a second one that is simpler and does not require to solve any linear system.

Jiahang Li on 25 Feb 2018

Dear Riccardo, It's a very interesting topic. It's a collection of notes.

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Problem 44531. 2) Are you more familiar with iteration methods or Linear Algebra ? Let's see together.

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