Let P₂(R) be the vector space of all real polynomials of at most degrees 2 with the inner product defined as (f, g) = f' [ Define T = L(P₂(R)) by T(ao + a₁x + a2x²) = a1x (a) Find an orthonormal basis B from the standard basis {1, x, x²}. (b) Find the matrix of T with respect to the orthonormal basis found in (a). (c) Show that T is not self-adjoint. f(x)g(x)dx.

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x − y, y - 2x), B' =…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

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A: Bartleby Guidelines:-“Since you have posted multiple questions, we will provide the solution only…

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A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

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Q: Let I2 ∈ M2(K) be the 2 × 2 identity matrix, where K is a field. For any A ∈ M2(K), let v1 =I2, v2…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

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Q: In the vector space of real functions on [-, π], let the inner product be defined by ㅠ (f,g) = f( […

A: Using the Gram-Schmidt orthogonalisation prosess to find an orthogonal basis.

Q: 1s) La L : A → R be the limsir operator Lip(z)) – p(0)r*+27/(c). Find the matrix A representing with…

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Q: orthonormal

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Q: 4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) =…

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Q: Find the limit. Enter DNE if the limit does not exist. lim (2,y) + (0,0) x² + 14y2

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Q: Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, 21 + 4x2)*:\\ i). Find the…

A: We have to find three matrix A B and P as described in the question.