Problem 2: If V=R3 is a vector space and let H be a subset of V and is defined as H={(a,b,c):c2+b2=0,a≥0}. Show that H is not subspace of vector space Problem 3 Let V=R3 be a vector space and let W be a subset of V, where W={(a,b,c):a2=b2}. Determine whether W is a subspace of vector space or not.

Question

Problem 2:  If V=R3 is a vector space and let H be a subset of V and is defined as H={(a,b,c):c2+b2=0,a≥0}. Show that H is not subspace of vector space  Problem 3  Let V=R3 be a vector space and let W be a subset of V, where W={(a,b,c):a2=b2}. Determine whether W is a subspace of vector space or not.

braodagxj · Accepted Answer

Problem 2:  V=R3  H={(a,b,c):c2+b2=0,a≥0}  At x=(1,0,0)∈H  But α=−2 is scalar in R  αx=(−2)(1,0,0)  =(−2,0,0)∉H(−2&amp;lt;0)  Not subspace of vector space V

Piosellisf · Accepted Answer

Problem 3:  V=R3  W={(a,b,c):a2=b2}  At x(1,−1,0)∈H  At y(1,1,0)∈H  But x+y=(2,0,0)∉H  ∴22≠02  Not subspace of vector space V