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Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

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Q: [6] 7. Let A = {1, 2, 3, 4, 5, 6}. Let R and S be the relation defined on A as follows: R = {(a, b)…

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Q: 2. Show that the scalar product of two vectors remains invariant at linear transformations of the…

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Q: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

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Q: 2) Let v be the rector space of matrices defined in R. 4 A=[ ethgiLED Find the coordmates of the…

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Q: -1 21 1 2 Show that A = 2 2. is diagonalizable by finding P and D such that P-'AP=D for a diagonal…

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Q: A2 A3 Ak A1, A2,... , An all invertible,

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Q: 29. Determinant of an Inverse Prove for invertible matrix A that

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Q: If uHu = 1 show that I -2uuH is Hermitian and also unitary. The rank-one matrix uuH is the…

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Q: 1. In the {li), j), Ik)} representation, the normalized basis vectors are chosen as li) = (1). 1) =…

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Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

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Q: и %3D-2, 1] -2u = [ Ex: 5

A: Step:-1 Scalar multiplication:- Let V = v1, v2  be any vector and let  "a" be any scalar then a.V…

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Q: A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal…

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Q: 5. Let M3 - {{: ahader} M22 = {" a la,b,c, de R Show that M22 with the usual matrix addition and…

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Q: 2.4 Use this matrix N to rotate the point (0, 3) an angle of 180° anticlockwise around the point (1,…

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Q: -6 V, = and v, = ,and let T: R2→R? be a linear transformation that maps x into x,v, + x,V2. Find a…

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Q: Suppose that G E Fxn. Let X1, X2, ...Xe be a basis for Nul(G). Form a matrix H whose columns are X1,…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…