Af a, B are two vectors in an inner product space V(F) and a, be F then prove that Re (a, B) = || a + BI? -|| a – BIP.

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Without using anything from the above two results show that for any complex inner- product (·, ·)v…

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Q: 1) Suppose Ris the set of real numbers, and we define addition (using the symbol ) as: x ® y =…

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Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1), (0,0,1,5)}, then…

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Q: Please solve this question with a good explanation. It is Linear Algebra question.

A: According to the given information it is required to show that zero vector in a vector space V is…

Q: с) Let A :1, →1, be defined by Ах, х, ...) %3D (0, 0, х2, Хд, .). Prove that A is self-adjoint,…

A: Please find the answer in next step

Q: (1,1,..., 1)T be the column vector consisting of all 1s. Prove 0. 3. Let a = that La

A: Given: Let a=(1,1,......1)T  Then objective is to prove  La=0

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Q: Let (V, (,)) be an inner product space and let f, g be vectors in V. If || F|| = 4. ||g|| = 5 and ||…

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Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

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Q: In words, explain why V is closed under addition and scalar multiplication. Since addition on V is…

A: According to the given information, first it is required to explain why V is closed under addition…

Q: 3. Let v, and v2 be vectors in an inner product space V. Show that ||v + v2||? < (||Vvl+ ||v2||)?

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Q: Е. Prove by induction that ||X1 + ·..+Xx|| < ||X1||+…+||x½|| for vectors x; in R".

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Q: (5) For every u in V, there is a vector in V denoted by u such that u + (-uu) = 0 O This axiom…

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Q: Find vector x and y in R? that are orthonormal with respect to the inner product (u, v) = 4u1v1…

A: Let x=14,0, y= 12,0 Hence, by using the given inner product, we have x,y=414(0)…

Q: Let TilP > Pz, the basis of NIT) T (ax²+bx+c) = 2Qx+ b. Then %3D is

A: Applying nullity definition we have

Q: Show that the vectors (1, 1, 2), (1,2,5), (5,3,4) of R'(R do not form a basis of R'(R).

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Q: There are Euclidean vector spaces with dimension 0 < dim < 00 that have no orthonomal basis. O TRUE…

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Q: 9. "Find two bases in the vector space R* (over R) such that the only vectors common to both are…

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Q: Find vectors x and y in R2 that are orthonormal with respect to the inner product (u, v) = 3u₁v₁ +…

A: The given problem is related with inner product. We have to find the vectors x and y in ℝ2 that are…

Q: 19. Show that there are infinitely many vectors in R# with Euclidean norm 1 whose Euclidean inner…

A: To prove:                 There are infinitely many vectors in R with Euclidean norm '1' whose…

Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ &amp; v→ Nonzero scalar α v→=αu→

Q: and ŷ = Find the values of y, and y, such that vectors = constitute an orthonorma L0.8337! basis in…

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Q: f || x, is Infinite norm of vector x on R then Al, = max Ax|, Select one: True False

A: We have to check whether the statement, "Given x∞ is infinite norm of vector x on Rn then…

Q: 7. Let S = Show that span S = R and find a basis for R' consisting of vectors from S. %3D

A: The solution is given as

Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

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Q: In a vector space V, prove that Ov = 0 For all VEV

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Q: Suppose V₁ is a vector of all entries 1 in R" space, which we call "1-vector". What is ||v₁||2 (12…

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Q: If Aj is a covariant tensor of the second order and Bi, Ci are contravariant vectors; prove that…

A: Given: Aij is a covariant tensor of 2ndorder To find: AijBiCj is an invariant tensor

Q: Let 12, v, w be vectors In an inner product space such that //u|| =5, ||v||=5, and (u, v) =-2. Use…

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Q: Given the standard basis {₁,..., en} for the real vector space R" complete with the product in…

A: Using the property of inner product.

Q: : If U, U₁, U₂ are 3 vectors in a vector space V such that v - 7v₁ + 3v₂ = 0. Then, u belongs to…

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Q: are vectors in R³ are linearly independent but ü,v,w are linear dependent. Show that there exist…

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Q: Let V = Rº. Give a definition of addition + or scalar multiplication on V that makes (V,+,-) unable…

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Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) : = 7 and |w| = 5,…

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Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

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Q: 2- Show whether the set of vectors S={ ,,} is a basis of R3 ?

A: Given the set of vectorsS={&lt;3,2,2&gt;,&lt;−1,2,1&gt;,&lt;0,1,0&gt;}

Q: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A).

A: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A). For any scalar k, we need to…

Q: 11. Let (V,(, )) be a complex inner product space. For vectors v, w, set (v, w)r = 1/[(v, w)+(w,…

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Q: Show that the vectors (1, 1, 2), (1, 2, 5), (5, 3, 4) of R'(R) do not form a basis of R'(R).

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Q: Suppose that &lt;*,*&gt;1 and &lt;*,*&gt;2 are two inner products on a vector space V. Prove that…

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Q: 49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a…

A: We prove that the set of vectors form a linearly dependent set.

Q: Suppose that two vectors T and ỹ in R" are orthogonal, meaning their inner product satisfies ·g = 0.…

A: This is a problem of vector calculus.

Q: show that a set of vectors{et cos(2t), e¯t sin(2t)} form a basis of solution space for x" + 2x' + 5x…

A: Substitute the value of x in the solution space and see if the value satisfies the equation, if the…

Q: Choose only one and write a concise proof. (a) Let A {u, U2.., U} and B = {n. v2.... Vs} be subsets…

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