Knowee
Questions
Features
Study Tools

rom the axioms of a vector space, prove that −(v + w) = (−v) + (−w), for all vectors v, w

Question

rom the axioms of a vector space, prove that −(v + w) = (−v) + (−w), for all vectors v, w
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

Sure, here is the proof:

  1. We know that for any vector v, v + (-v) = 0. This is the definition of additive inverse in a vector space.

  2. Now, consider the vector v + w. Its additive inverse is -(v + w), which means (v + w) + (-(v + w)) = 0.

  3. We also know that vector addition is associative, so Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  

This problem has been solved

Similar Questions

rom the axioms of a vector space, prove that −(v + w) = (−v) + (−w), for all vectors v, w

Let v be a vector and let k be a scalar. From the axioms of a vector space, prove that if kv = 0 theneither k = 0 or v = 0.

Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).

Suppose {v,w} is a linearly independent set in the vector space V.Then the set {v,v+w} is also linearly independent.A. TrueB. False

Let u, v and w be vectors in R3. Which of the following calculations is possible? (a) u + (v · w) (b) u · (v × w) (c) (u · v) × w (d) u × (v · w)

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.