Show that each of the following are not inner products on R³,

Q: Let а 3 (1,0, —2). 6 = (3, 1, –1). č = (1,0, –1). - Find the triple scalar product ā o (b × č), and…

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Q: 1 2 3 2. Give an algebraic specification for the null space and the column space of A =2 5 4 107…

A: The column space of a matrix A is the vector space made up of all linear combi­nations of the…

Q: A (real or complex) scalar u is said to be an nth rootof unity if un = 1. Show that if j and k are…

A: To prove this If j and k are positive integers,

Q: Find bases of for the column space of A, row space of A, and the null space of A 1 1 -1 0 2 -2 A = 2…

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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: Let ((u,,u2,U3),(V1,V2,V3))= 2u, V1 + 3u2V2+ U3V3 be an inner product on R. Determine ||(1, – 1, -…

A: Explanation of the answer is as follows

Q: 2. Let z be a complex number. Prove the following identities. a) zz* = |z|2 b) Im(z+ z*) = 0 c) (2 +…

A: We are entitled to solve only one question at a time and up to 3 sub-parts only. Please post another…

Q: Prove that if A ∈ M 2×2(F) is upper triangular, then det(A) equals the product of the diagonal…

A: Let the matrix A be the upper triangular matrix as follows.

Q: Let A E R"Xn. Show that =, Vx, y E R" iff A = A'. Show this inner product equality holds for A E Cxn…

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Q: Find the scalar triple product u.(v x w) if u = 3i - 2j - 5k; v = i + 4j - 4k; and w = 3j + 2k. And…

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Q: Let V be an inner product space over the complex numbers C with the inner product defined as (u,v〉 =…

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Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: x · y = (x + y² – x² - y²)

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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…

Q: In the 2D space there are 2 iterated integrals. In the 3D there are 6 iterated integrals. How many…

A: Recall:         n!=n(n-1)(n-2)...3.2.1

Q: Sketch each of the following Cartesian products using separate figures for each Each is subset of…

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Q: 7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the…

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Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

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Q: Give C the standard inner product. Calculate ||(2+3i, 1+i)||.

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Q: Show that both ℝ and ℝ2 may be covered by countably many open spheres.

A: We have to show that  and  covered by countably many open balls.

Q: Find a zero-divisor in Z,[i] = {a + bi | a, b E Z3}.

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Q: If A is diagonalizable (i.e. C CAC = D), then calculate A*.

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