970.3046070.qx3zqy7 Jump to level 1 Let {u₁(x) = − 12, u₂(x) = − 12x, uz (x) = 8x²} be a basis for a subspace of P2. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (f, g) C[0, 1]. › = √² Orthogonal basis: {v₁ (x) = −12, v₂(x) = -12x + a, v3 (x) = 8x²+bx+c} a = Ex: 1.23= b = Ex: 1.23 c = Ex: 1.23 [ f(z)g(2) da on 5

Q: 4. Consider the subspace V of R' given by 3 V = span (a) Find an orthonormal basis for the…

A: vector subspace  V  of  ℝ4  given by ,               V = span 1001 , 31-11 (.)  If  W be a subspace…

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Q: Let -0-0 and b -4 Use the Gram-Schmidt procedure to determine an orthonormal basis {q₁, 9₂} for the…

A: Here we have to determine orthonormal basis {q1 , q2 } using gram schmidt process.

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Q: Let the transformation of P2 -> P1 be defined as T(p(t)) = p'(t). The basis B = {1,t,t^2} and S =…

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Q: Let {u₁(x) = 12, u₂(x) = − 18x, uz (x) = 8x²} be a basis for a subspace of P2. Use the Gram-Schmidt…

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Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: 2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a…

A: Given matrix A=111213 AT=111123

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Q: i 9. A= |-i 1 - i 1+ i 8. Use gram-schmidt to find the orthogonal basis for the four fundamental…

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Q: 3. Let S be the subspace of R' given by S = {(x1, x2, T3, T4) : x1 – 2x2 + 4.x3 – 3x4 = 0} %3D - a.…

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Q: (b) Calculate a basis C for S and state dim(S).

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Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

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Q: Let 3 -7 ,V = u -3 -3 4 and let W the subspace of R* spanned by u and v. Find a basis of w', the…

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Q: 1. Given: 1. Vector = (1,1,1) (in standard basis) 2. The linear transform (in standard basis) T: R→…

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Q: Let x = -2 and y =| -3 -3 Use the Gram-Schmidt process to determine an 3 orthonormal basis for the…

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Q: Let {u1 (x) = 12, u2 (x) = 12x, u3 (x) = 8x² } be a basis for a subspace of P2. Use the Gram-Schmidt…

A: Orthogonal basis, therefore inner product will be zero for distinct two elements.

Q: = = 12, u₂ (x) = 18x, uz (x) = − 8x²} be a basis for a subspace of P₂. Use the Gram-Schmidt Let {u₁…

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Q: (c) Let M = (xn)el² :x, + x, = 0}. Show that M is a closed subspace and find an orthonormal basis…

A: Please check step 2 for the solution.!