Write a linear equation defining the subspace of R_3 spanned
Write a linear equation defining the subspace of spanned by and . (Write your answer in the form ax+by+cz. For example "2x+3y-4z") I have this question to solve, but I don't have any idea how to solve this. Help me.
Every element of your linear subspace can be written as a linear combination of and . If and both satisfy
then so does any linear combination of the two. Since span a 2 dimensional subspace of a 3 dimensional space, we only need one equation to describe it, and both and must solve it. So we need
Solving these equations gives (a,b,c) up to some factor that we can choose, since
have the same solution set if