Question

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

x1 + 2x2 + 5x3 = 7

Answer 1

it is 2-d plane

Answer 2

I get \[\left(\begin{matrix}x1 \\ x2\\ x3 \end{matrix}\right)\] = x2 * \[\left(\begin{matrix}-2 \\ 1\\ 0 \end{matrix}\right)\] + x3* \[\left(\begin{matrix}-5 \\ 0\\ 1 \end{matrix}\right)\] + \[\left(\begin{matrix}7 \\ 0\\ 0 \end{matrix}\right)\] so im guessing that's the algebraic answer? Just not sure how this looks geometrically.