# Linear Functionals and the Dual Space

May 29th, 2015
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11.21 Find the dual basis of each of the following bases of (ii)

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Esterlina Angela Juliana1113150007FKIP Pendidikan MatematikaUniversitas Kristen IndonesiaCHAPTER 11: Linear Functionals and the Dual Space11.19Let and be the linear functional defined by and Find :i. ii. 3311.21Find the dual basis of each of the following bases of (ii) We seek linear functionalsuch thatWe find as followsSolving the system of equations, we obtain Thus We next find Solving the system of equations, we obtain Thus Finally, we find Solving the system of equations, we obtain Thus 11.31Let W be the subspace of spanned by Find a basis of the annihilator of WBy the preceding problem, it suffices to find a basis of the set of linear functional for which The system of equations in unknowns a, b,c, d is in echelon form with free variables c and d.Set and to obtain the sol

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