Unformatted text preview: Find a matrix representation for the operator L of the previous exercise. Solve the same exercise using only linear algebra. Problem 7 Find the matrix of the linear transformation L : R 2 → R 2 such that L ([1 ,√ 3] T ) = [0 , 0] T and L ([ √ 3 , 1] T ) = [3 , √ 3] T . Problem 8 Find the solutions of the equation z 3 = 1 + i . Problem 9 Find the real Fourier coeﬃcients a ,a 1 ,a 2 of the functions f,g,h deﬁned by f ( x ) = µ1 if x ∈ (π, 0] 1 if x ∈ (0 ,π ] ; g ( x ) = cos(23 x ); h ( x ) = µ if x ∈ (π, 0] 1 if x ∈ (0 ,π ] ....
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 Winter '09
 Linear Algebra, Polynomials, diﬀerent PLU decompositions

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