6. Let function f(x) be defined for -L sx sL. The Fourier series of f(x) isFind the coefficients of the Fourier series for the function f(x)= x -π ≤ x ≤ π .

5. Let matrix that is composed of tirere column vestors Find the QR-decompostion of A, ie, A=OR where Q is a 3xs matix with ortionormal colann vectors and R is a 3x3 invertible upper triangular matrix. Hint: use Gram-Schmidt process to transform the basis vectors of the three column vectors in A into an orthogonal basis, and then normalize the orthogonal basis vectors to obtain an orthonormal basis corresponding to the column vectors q1,q2,q3 in matrix Q. The entry of matrix R is the inner product of vectors .

6. Let function f(x) be defined for -L sx sL. The Fourier series of f(x) is

Find the coefficients of the Fourier series for the function f(x)= x -π ≤ x ≤ π .

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