Question

(b) Let H be the subset of R3 consisting of all points that can be expressed 2 in the form y where x is any real number, and y is any real number 31 such that y > 0. Is H a subspace of R3? Be sure to support your claim! (5 points)

Answer 1

and h is © let H be a subset of R3 expressed in the form ra] real number and y>o. 1 a eR. where xyn any 1. that H n a subspace of R3 or now we check not. het any 132 li d = I and ßal ninibe any real and yiZO, where borette a BEH. now &#8 = freem yen T [xxx2 , - | tv [ 324 +342 [3c4px)} 4 and a be real number number therefore (4+4) be also real y o and 270 this implies yay20. now and x+B = F4 +x27 13+ DE | 342448) Eh since and 64722) belongs for +42) >0 since 4,30_220, so a EH, BEH » KABEH 13 ley 21 and consider ca where e be any scalar (40). from frield R. so caz csa *,y be any real number and yo. 3) lezzy) [Buku) now y be any real number and CER this implies cry also read number, and Yayo (YO (10) when c>,O. but when cer and eco then cyço.

so H is not a therefore ath but ca elt subspace of R3 bor example a x = TEH done and - 2ER 121 . then then -2* = -20 = 6ot belongs to hot belongs to t -4. L-3.2] W so it is not a subspace of IR?