Write a linear equation defining the subspace of R_3 spanned

horrupavinvo

horrupavinvo

Answered question

2022-02-22

Write a linear equation defining the subspace of R3 spanned by v1=(0,0,2) and v2=(3,1,1).
(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.

Answer & Explanation

lilwayne10j6o

lilwayne10j6o

Beginner2022-02-23Added 8 answers

Every element of your linear subspace can be written as a linear combination of v1 and v2. If (x1,y1,z1) and (x2,y2,z3) both satisfy
ax+by+cz=0
then so does any linear combination of the two. Since v1,v2 span a 2 dimensional subspace of a 3 dimensional space, we only need one equation to describe it, and both v1 and v2 must solve it. So we need
a0+b0+c2=0
and
a(3)+b(1)+c(1)=0
Solving these equations gives (a,b,c) up to some factor that we can choose, since
ax+by+cz=0
and
kax+kby+kcz=0
have the same solution set if k0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?