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For example: if I have a solution like [2r10 + 2r9, x_2 == r10, x_3 == -2r9, x_4 == r9]] how can I transform that in vector V V= [2r10 + 2r9, r10,-2r9, r9]]]

For example: you solve a linear system (in sagemath) with infinite solution and you get:

[2*r10 + 2r9, 2*r9, x_2 == r10, x_3 == -2r9, -2*r9, x_4 == r9]]
how 

How can I transform that in vector V V= [2r10 extract the vector

V = [2r10 + 2r9, r10,-2r9, r9]]]2r9, r10, -2r9, r9]

Any suggestion to find a dimension of the solution space for system with infinite solutions as above using Sage?

For example: you solve a linear system (in sagemath) with infinite solution and you get:

[2*r10 [[x_1==2*r10 + 2*r9, x_2 == r10, x_3 == -2*r9, x_4 == r9]]

How can I extract the vector

V = [2r10 + 2r9, r10, -2r9, r9]

Any suggestion to find a dimension of the solution space for system with infinite solutions as above using Sage?

For example: you solve a linear system (in sagemath) with infinite solution infinitely many solutions and you get:

[[x_1==2*r10 [[x_1 == 2*r10 + 2*r9, x_2 == r10, x_3 == -2*r9, x_4 == r9]]

How can I extract the vector

V = [2r10 + 2r9, r10, -2r9, r9]

describing these solutions?

Any suggestion to find a the dimension of the solution space for a system with infinite infinitely many solutions as above using Sage?

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

[[x_1 == 2*r10 + 2*r9, x_2 == r10, x_3 == -2*r9, x_4 == r9]]

How can I extract the vector

V = [2r10 [2*r10 + 2r9, 2*r9, r10, -2r9, -2*r9, r9]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

[[x_1 
solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)
 
[[x == 2*r10 + 2*r9, x_2 2r1 - 2r2, y == r10, x_3 r2, z == -2*r9, x_4 -2*r1, w == r9]]

How can I extract the vector

V = [2*r10 + 2*r9, r10, -2*r9, r9]
[2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)

[[x == 2r1 - 2r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I"m I'm new a user...

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w') sage: solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)

sage: [[x == 2r1 - 2r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I'm new a user...

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w') sage: w'); solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)

sage: [[x == 2r1 - 2r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I'm new a user...

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w'); solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)

[[x == 2r1 - 2r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I'm new a user...

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w'); solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)

[[x == 2r1 - 2r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I'm new a user...

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w'); solve([x+2y+2z+2w==0, 2x+4y+6z+8w==0, 3x+6y+8z+10*w==0], x,y,z,w)
 
solve([x+2*y+2*z+2*w==0, 2*x+4*y+6*z+8*w==0, 3*x+6*y+8*z+10*w==0], x,y,z,w)
[[x == 2r1 2*r1 - 2r2, 2*r2, y == r2, z == -2*r1, w == r1]]r1]]

V = [2*r1 - 2*r2, r2, -2*r1, r1]

For example: solve a linear system (in sagemath) with infinitely many solutions and get:

sage: var('x y z w'); solve([x+2*y+2*z+2*w==0, 2*x+4*y+6*z+8*w==0, 3*x+6*y+8*z+10*w==0], x,y,z,w)
w')
sage: eqq = [x + 2*y + 2*z + 2*w, 2*x + 4*y + 6*z + 8*w, 3*x + 6*y + 8*z + 10*w]
sage: solve(eqq, x, y, z, w)
[[x == 2*r1 - 2*r2, y == r2, z == -2*r1, w == r1]]

How can I extract the vector

V = [2*r1 - 2*r2, r2, -2*r1, r1]

describing these solutions?

Any suggestion to find the dimension of the solution space for a system with infinitely many solutions as above using Sage?

PS. I'm sorry if the question is too trivial, I'm new a user...