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LetU={(z1, z2, z3, z4, z5)C:6z1=z2, z3+ 2z4+ 3z5=0}.CheckifUisasubspace.IfUisasubspace,thenfindabasiswhich spanU.(b)Supposeb1, b2, b3, b4is a basis of vector spaceV.Prove thatb1+b2, b2+b3, b3+b4, b4is also a basis ofV.

LetU={(z1, z2, z3, z4, z5)C:6z1=z2, z3+ 2z4+ 3z5=0}.CheckifUisasubspace.IfUisasubspace,thenfindabasiswhich spanU.(b)Supposeb1, b2, b3, b4is a basis of vector spaceV.Prove thatb1+b2, b2+b3, b3+b4, b4is also a basis ofV.

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