Question

D Linear Algebra Summer il Week N Netflix Link for today's lesson - MATH X > со .youtube.com/watch?vhoC4Eva Sew Q Search YouTube Linear Algebra Quis 12 Show that the following is a subspace : W = - {axx*/2*, *** ID 0:56/54:46 ce F Linear Algebra Summer 1 Week 4 Lesson 12 ca Unlisted No views .Jul 23, 2020 bo GO SHARE + SAVE Type here to search RI

Answer 1

a) Non-empty : Since (1,2) belongs to this set, it is Non-empty

b) Closure property of Addition : Suppose (x1,x2) and (x3,x4) are in this set then x2 = 2(x1) , x4 = 2(x3) , adding these two, x2 + x4 = 2(x1 + x3) , so (x1+x3,x2+x4) also is in this set

c) Property of scalar multiplication : Suppose (x1,x2) is in this set and k is some scalar. Then since x2 = 2(x1) , multiplying both sides by k, we get k(x2) = k(2(x1)) = 2(k(x1)) . So (k(x1), k(x2)) also is in this set.

So it is a subspace.