Let V be the space of real polynomials defined on the interval [-1, 1]. The inner...

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Let V be the space of real polynomials defined on the interval [-1, 1]. The inner product is defined to be (PQ) = ¹, P(x)Q(x)dr. Starting from the non-orthonormal basis R. (r) = 2¹ (for i = 0,...), use the Gram-Schmidt procedure to construct the first four vectors in an orthonormal basis. Let V be the space of real polynomials defined on the interval [-1, 1]. The inner product is defined to be (PQ) = ¹, P(x)Q(x)dr. Starting from the non-orthonormal basis R. (r) = 2¹ (for i = 0,...), use the Gram-Schmidt procedure to construct the first four vectors in an orthonormal basis.