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## Homework Statement

Bonus] Let E = {“ax+by+cz = d” | a; b; c; d ∈ R} be the set of linear equations

with real coeﬃcients in the variables x, y and z. Equip E with the usual operations

on equations that you learned in high school: addition of equations, denoted here

by “⊕” and multiplication by scalars, denoted here by “~”, as follows:

“ax + by + cz = d” ⊕ “ex + fy + gz = h” = “(a + e)x + (b + f)y + (c + g)z = d + h”

and

∀k ∈ R; k ~ “ax + by + cz = d” = “ka x + kb y + kc z = k d”:

You may assume without proof that E is a vector space.

Find a spanning set for E.

(You must justify your answer.)

## Homework Equations

## The Attempt at a Solution

I have no idea what this question is asking...isnit the span just span{x,y,z}? o.o