Suppose TEL(V) has singular value decomposition given by Tv = $₁(v. e₁) f₁ +...+ Sn(v.en) fn for every ve V, where $₁.... Sn are the singular values of T and e₁.....en and fi..... fn are orthonormal bases of V. (d) Suppose T is invertible. Prove that if ve V, then (v. fn)en T-¹y = (v. fi)ei $1 + + Sn for every v € V.

Q: 59. In R4, given 2 nullspaces 1 2 00 1 V : |-1 0 -1 m 0- Find m such that dim(U n V) is max. Find…

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Q: 16. Consider the vectors [1/2] 1/2 1/2 1/2] 1/2] 1/2 -1/2 [-1/2] 1/2] -1/2 1/2 --1/2] ü2 = üz = in…

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Q: Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-

A: Given that The transformation is

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A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

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A: W need to find elements which are invertible inZ4x,y.

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: 201 Give monsingural uragonal matrix. Call a diagonal matrix ever be 21) Show that ( (2) where x, y,…

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A: According to the given information,

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A: Option (a) is correct

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Q: Find a norm of the operator A(x) = (t³ + 2t2)x(t) in space C[0, 1]. O a. 3 O b. 4 7 2 3 O d. 6 O e.…

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Q: -13/27] -4/27 -4/9 5/9 -20/27] -2/27 Let v₁ = √2 = and √3 = Find a vector in IR4 such that -20/27 '…

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Q: (5) Let T P₂ → P₁ represented by T(ao + a₁ + a₂x²) = a₁ + 2a₂x. Find kernel of T.

A: We have to find kernel of T.