5. v-tv l closed under the defined operations of addition and scalar multiplicat

Question

5. v-tv l closed under the defined operations of addition and scalar multiplicationl is a Vector Space U-span ev; rv. yu Linear combination by all vectors in this group of U (may be can be shinked to a group of basis vectors EU and then inherits all othe properties of v s v U is vs. and called as sub space of V Since (0) 1. R' is a V.S. i 2. i 0. j 1 ER', spanti, ji vitv vz -ve "x-plane" is a In V.S. R. or R' x-axis 3. In V.S.R Basis and Dimension of a V.S. or sub-space. As a example: the basis of R set. If tv,... v.1 uniquely generales each vector in a vector spacev, len v.Bis a LI v. uniquely generates each v e v. that is 3lf, o x x.v. v The set V solution, so lv .]-1.. is tv,...v. is a LI set. [v,...v.K v has unque that v If tv v. is a set, the tv .1 uniquely generates each vector V in LI solution lvi...v.lv vl ....v.lis a set, then lvi...V. l so for w v E v, lvi...V.R has unique Is tv .....v. uniquely generates each vector v in v If fv is a Lu set and V spant vi.....v, we call tv v.; is a any basis as of V .....v,1 The basis of V may be not unique, but the number of the LI ectors in any bases are same, call the size of so vanishes. 14 1is a basis, then one more in tv must be linearly expressed by and be IA/M 2017mid or v, from ti,... v.) is LI set, can not be generated by tv .1 which can not say, a basis of V.

Explanation / Answer

2- subspace of R3 ,(by defination )

3- subspace of R3 ,( again by defination)

4- basis of V ,( as the largest linearly independent set and largest spanning se is called basis so its basis)

5- dimension of V (as no of basis is known as the dimension of vector space)

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