chillywilly12a

2021-02-09

Determine if
$a.H=\left\{\frac{x,y}{y}=3x-1\right\}$ is a subspace of R2
$b.H=\left\{at+\frac{b}{b}=8a\right\}$ is a subspace of P1

delilnaT

Let V be a vector space and $S\subset V$ is said to be a subspace of V if the followings holds
$0\in S$ for u,$v\in S$ and for a scaler k $u+kv\in S$.
(a)Here it is given $H=\left\{\left(x,y\right):y=3x-1\right\}.$ Since (0, 0) is not in H. Thus H is not a subspace of ${R}^{2}$.
(b)Here it is given $H=\left\{at+b:b=8a\right\}.$ Clearly (0, 0) is in H. Let $at+b,ct+d\in H$. Then . Now for a scaler k

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