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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Deepak Patra posted an Question
December 25, 2021 • 15:45 pm
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30 points
30 points
- IIT JAM
- Mathematics (MA)
4. let denote a vector space over a field f and with a basis b=l.e2,..,en let ,*2,x, ef let c={mx1 +x2e2 +x22t.**nn . then (a.) c is a linearly independent set
4. Let denote a vector space over a field F and with a basis B=l.e2,..,en Let ,*2,X, EF Let C={MX1 +X2e2 +X22t.**nn . Then (a.) C is a linearly independent set implies that x; *0 for every i =1,2,..,n (b.) x *0 for every i=1,2,...,n implies that C is a linearly independent set. (c.) The linear span of C is V implies that x #0 for'every i = 1,2,..,n (d.) x; *0 for every i=1,2,..,n implies that the linear span of C isV
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sir please explain option c and d
c is LI subset of V of dimension n so by extension th it is basis of V linear Span of v