IIT JAM
   Top Resources
Shweta posted an Question
January 11, 2020 • 18:49 pm 15 points
  • IIT JAM
  • Mathematics (MA)

Let R be the set of positive real numbers. if the operation of vector addition and scalar multiplication is defined as followsu+V=uv for all uv€ R" and c.u = u

Let R be the set of positive real numbers. if the operation of vector addition and scalar multiplication is defined as followsu+V=uv for all uv€ R" and c.u = u for all uER" and real scalar c R (R) is a vector space R (R) is not a vector space as there is no additive identity R (R) is not closed under scalar multiplication none of these

1 Answer(s) Answer Now
  • 0 Likes
  • 2 Comments
  • 0 Shares
  • Priyadarshan Choursiya Best Answer

    one can prove, Lhs=rhs by solving for Lhs and rhs then check they are equal or not. here I also explain the abelian group in part (i). solution is only look big, because I explain everything but when a IIT inspire do that question so he leave some things which are look easily. here I also explain method to find identity and inverse. you also know that. (R,+) is a group, so sometimes I use the groupness of R, which I explain in solution. when we perform any operational for any element of G then that this operation is true for every of its elements. here I only find left identity and inverse, you need to find right, as I find left. and chack that left=right. if they are not equal so it is not identity or inverse respectively. note that here they are equal. to prove it a vector space it is must essential to know you that when we use usual operations and when we use given operations. here I explain them in some places.

    upload_1578746239079.jpg
    upload_1578746250353.jpg
whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers

Sign Up to Download FREE Study Material Worth Rs. 500/-