Describe the solution set in R^3 of the system both algebraically and geometrically:

x1 + 2x2 + 5x3 = 7

I think i got it algebraically as

(x1,x2,x3) = x2(-2,1,0) + x3(-5,0,1) + (7,0,0)

but how do i describe this geometrically with x2 and x3 being free variables?

are (-2,1,0) and (-5,0,1) vectors on the plane that goes through (7,0,0) ?

Question

Describe the solution set in R^3 of the system both algebraically and geometrically:

x1 + 2x2 + 5x3 = 7

I think i got it algebraically as

(x1,x2,x3) = x2(-2,1,0) + x3(-5,0,1) + (7,0,0)

but how do i describe this geometrically with x2 and x3 being free variables?

are (-2,1,0) and (-5,0,1) vectors on the plane that goes through (7,0,0) ?

anonymous · Answer

You can interpret it as a set of points in space that passes through (7, 0, 0) summed with a linear combination of vectors (-2, 1, 0) and (-5, 0, 1).

(If your answer is correct... I didn't check)