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**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 coecients a ,a 1 ,a 2 of the functions f,g,h dened by f ( x ) = -1 if x (-, 0] 1 if x (0 , ] ; g ( x ) = cos(23 x ); h ( x ) = if x (-, 0] 1 if x (0 , ] ....

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