Determine if a. H={(x,y)/ y=3x-1} is a subspace of R2 b. H={at+b/ b=8a} is a subspace of P1

chillywilly12a 2021-02-09 Answered
Determine if
a.H={x,yy=3x1} is a subspace of R2
b.H={at+bb=8a} is a subspace of P1
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Expert Answer

delilnaT
Answered 2021-02-10 Author has 94 answers

Let V be a vector space and SV is said to be a subspace of V if the followings holds
0S for u,vS and for a scaler k u+kvS.
(a)Here it is given H={(x,y):y=3x1}. Since (0, 0) is not in H. Thus H is not a subspace of R2.
(b)Here it is given H={at+b:b=8a}. Clearly (0, 0) is in H. Let at+b,ct+dH. Then b=8a and d=8c. Now for a scaler k

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