Author: Study Clue

a Which statement matches “closure under addition”? A Product stays in set B Sum stays in set C Inverse always

For W={(x,y,z)∈R3:x+2y+3z=0}W={(x,y,z)∈R3:x+2y+3z=0}, dim⁡(W)dim(W) is A B. 1 B C. 3 C A. 2 D D. 0 Explanation Explanation: A single

For W={(x,y)∈R2:x+y=0}W={(x,y)∈R2:x+y=0}, which is true? A Not closed addition B Not closed scalar C Subspace of R2R2 D Missing zero

Which subset of R2R2 is a subspace? A Line not through B Line through origin C Circle centered origin D

Which item must exist in a vector space? A B. Prime element B C. Division operation C D. Order relation

If |G|=pq with p<q primes and p ∤ (q−1), then G is A simple B nonabelian always C no subgroups

In a group, (a⁻¹)⁻¹ equals A e B a⁻² C a² D a Explanation Explanation: The inverse of a⁻¹ is

If a has order 6, then a³ has order A 3 B 6 C 1 D 2 Explanation Explanation: In

In a group, cancellation law means A ab=ba always B a+b=a only C a²=a always D ab=ac ⇒ b=c Explanation

Which property means “a*b is in G” for all a,b in G A Identity B Closure C Inverse D Commutative