Consider P under the inner product: (p(x) q(x)) = p(-2)q(-2)+p(0)q(0)+p(1)q(1) +p(2)q(2). Construct an orthonormal set {ui(x),...

 

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Consider P³ under the inner product: (p(x) q(x)) = p(-2)q(-2)+p(0)q(0)+p(1)q(1) +p(2)q(2). Construct an orthonormal set {ui(x), u2(x), u3(x), u(x)}, where u₁(-2) = 1, u1(0) = 0, u(1) = 0, u(2) = 0, u2(-2) = 0, u2(0) = 1, u2(1) = 0, u2(2) = 0, and so on. In other words, u(x) is analogous to e₁ = (1, 0, 0, 0), u2(x) is analogous to ez (0, 1, 0, 0), u(x) is analogous to e3, and u4(x) is analogous to e4. = Consider P³ under the inner product: (p(x) q(x)) = p(-2)q(-2)+p(0)q(0)+p(1)q(1) +p(2)q(2). Construct an orthonormal set {ui(x), u2(x), u3(x), u(x)}, where u₁(-2) = 1, u1(0) = 0, u(1) = 0, u(2) = 0, u2(-2) = 0, u2(0) = 1, u2(1) = 0, u2(2) = 0, and so on. In other words, u(x) is analogous to e₁ = (1, 0, 0, 0), u2(x) is analogous to ez (0, 1, 0, 0), u(x) is analogous to e3, and u4(x) is analogous to e4. =

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To construct an orthonormal set u1x u2x u3x u4x under the given inner product we nee... View the full answer