Find a basis from cartesian equations

08312017, 07:06 PM
Post: #1




Find a basis from cartesian equations
Hello
I want to find an easier way to find vectors which are a basis of a vector space defined by cartesian equations. For eixample: x1+2x2+x3+2x4+x5=0 x12x2x4+2x5=0 x1+2x2+3x3+4x4+7x5=0 So, first I reduce the system (applying Gauss reduction): I use RREF(matrix of coefficients of the system) rref([[1,2,1,2,1],[1,2,0,1,2],[1,2,3,4,7]]) to obtain [[1,2,0,1,2],[0,0,1,1,3],[0,0,0,0,0]] So we have two equations which means the subspace represented have 52 dimensions. So for a basis of this space we need three independent vectors. Next I use solve() giving values to find three possible vectors: solve([[x1+2*x2+x42*x5,x3+x4+3*x5,x2 = 1,x4 = 0,x5 = 0]],[x1,x2,x3,x4,x5]) which gives {[2,1,0,0,0]} So I will change values for x2=0, x4=1 and X5=0 which gives {[1,0,1,1,0]} And third and last I change x2=0, X4=0 and X5=1 which gives {[2,0,3,0,1]} This is a very complicated way, to obtain the three vectors of the basis. Is there a function to solve this directly? Thanks for your help Toni 

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Messages In This Thread 
Find a basis from cartesian equations  Tonig00  08312017 07:06 PM
RE: Find a basis from cartesian equations  AlexFekken  09012017, 10:04 AM
RE: Find a basis from cartesian equations  Helge Gabert  09012017, 02:34 PM
RE: Find a basis from cartesian equations  Tonig00  09012017, 08:14 PM
RE: Find a basis from cartesian equations  Tonig00  09042017, 12:26 PM
RE: Find a basis from cartesian equations  parisse  09062017, 06:01 AM

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