Math  /  Algebra

QuestionSubspaces
1. Show that the sets consisting of vectors of the following form are subspaces of R2\mathbf{R}^{2} by showing that they are closed under addition and under scalar multiplication. (a) (a,3a)(a, 3 a)

Studdy Solution
Verify closure under scalar multiplication:
Consider an arbitrary vector (a,3a)(a, 3a) from the set and a scalar cc. The scalar multiplication is:
c(a,3a)=(ca,3ca)c \cdot (a, 3a) = (ca, 3ca)
Since (ca,3ca)(ca, 3ca) is of the form (a,3a)(a', 3a'), the set is closed under scalar multiplication.
The set consisting of vectors of the form (a,3a)(a, 3a) is a subspace of R2\mathbf{R}^2.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord