Let V be the vector space of all polynomials, with inner product < f,g >= | f(r)g(x)e¯*dx Let W be the subspace of V spanned by {1,r, r²}. (a) Use Gram-Schmidt to orthogonalize {1, r, r2}.

Q: Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O…

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Q: Let R be the field of real numbers. Then {(x,x,x): x ER}is a subspace of R (R) ?

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Q: (b) If V = R", and U is a subspace of V of dimension m with 0 <m <n, prove that U² = {v € V: B(u, v)…

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Q: .

A: Here we have to find an orthonormal basis for the subspace spanned by 1, x, x2:

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A: The correct option is c . i.e. w is a subspace of ℝ3.

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A: We have to find the orthonormal basis for Span(1,x,x2)

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Q: Let W fa + bx + cx2 + dx'| a+ b 0 and c-3d 0 } be a subspace of Pg. %3D %3D %3D Then the dimension…

A: a+b=0  and c-3d=0 b=-a and c=3d Equation given is; a+ bx+ cx2+ dx3  = a- ax+ 3dx2+ dx3 that can be…

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A: Orthonormal basis of W will be vectors vi|vi,vj=0; i≠j1; i=j.

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Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

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A: Let P5(x) be the standard vector space for polynomials of degree≤5. and U be the set of all…

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Q: Let f be a function in C[-T, 1] with inner product (f,g) = Sf(x)g(x)dx and W be a subspace spanned…

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Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to

A: Here we will find out dimension of W.

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Q: Consider the vector space C[-1, 1] of continuous functions on [-1,1] with inner product (f:9) = |…

A: The main objective is to find orthonormal basis by using gram smith orthogonalization.