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Requirements - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

Nalanda Open UniversityLinear Algebra

This is the Quiz Solution of Linear Algebra. Mainly include Row Operation, Resulting Matrix, Requirements, Reduced Row Echelon, Reason, Particular Solution etc. Key important points of tags are: Requirements, Subset, Vector Space, Subspace, Basis, Nul, True or False, Counterexample, Spanning Set, Three Vectors

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

seshu_lin3
seshu_lin3 🇮🇳

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MATH 205: Quiz 4 Name: ke 1. What are the three requirements for a subset H of a vector space V to be a subspace? ) GeH (zew vecbr isin H) (>) For any ve WH, @ePeH (closed under addit'on) i) For ong @EHFCEIR, CEH (closed under scalar muHiphica hon ) 1 Oo 1 = ol : = i, 6 Nul(P) i xq, us free Me BS Nul(B)= Xq] Gf + Xs] -1 2. Find a basis of the Nul(A) and ColfA). ioe 2 a 3 6 1 A=]2 -2 1 O 38 | andrref(A)=] 0 SSS ted 0 ous 0 0 1 one Xa Se ee i o Mao Ag oO : j 2 = basis for Nul(B)= Ee aS pik Col\(A) : 2pand Whe Xa 4 xs$ by def. huscafor Cotta)> £4] [a] [2] § 3. Write True or False. If false, give a counterexample. Te a Ce spans, but 1's nat % bass5, (oy A tacie ie divas bepaunine bet , True. (c) For R®, any set of three vectors is a basis. J a 1¢ 3 oO e 2 + The 5 (8, FFI) [3 False, IR lis pet a ass.