General Solution-Three variables-Two Equations

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Homework Statement



Find the general solution of the following set of equations:

u − w + y = 1
u + w + 2y = 0

Homework Equations





The Attempt at a Solution



I know that the solution is in this form (u,w,y)= (a,b,c) + k*(d,e,f)

Can you please explain me how i am going to find it?
 
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hi mikael27! :smile:

there are several ways to do this

one is to see that each equation represents a plane (in ordinary 3D space)

so their intersection is a line …

how would you find the direction of that line? :wink:​
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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