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: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

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Q: If V is a vector space then show that cV=V.

A: Vector space: A non-empty set V closed with two binary operations called addition and scalar…

Q: Q2 (a) Let n E N and let 7, w e R". Show that if ở - = 0, then || † + w||? = || T||? + ||||?. (b)…

A: To answer the given question we shall use the following rule: 1.   If x→∈ℝn, then…

Q: Given that {an, 92, 93, any is a linearly independent set of vectors in a Vector space • V'( note…

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Q: In a vector space V, prove that (-1)v= -v for all v E V.

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Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

Q: (c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the…

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

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Q: 1. Let, p is the set of all vectors of the form: m,n, te R. 2n (a) Is p closed under vector…

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Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: Let  W = { (a, b) : a and b are real numbers, a + b =1 } . For any (a, b) and (c, d) in W and…

A: W={(a,b): a and b are real numbers, a+b=1} Since every vector space is a group under addition. If W…

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

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Q: Consider the set V = R − {2}, that is, the set of all real numbers except 2. Define “addition” as…

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Q: C: Let A = (v₁,..., v4) be any list of 4 vectors in the vector space V. Let B = (v₁-V2, V₁-V3,…

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: Show that the set of complex number C={x+iy|x and y are real, i2=-1} is a vector space. Verify each…

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Q: s an inner product space, where (a, 5) = 4 – 5i.

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Q: Let vector a and vector b be 2 vectors  a) show that |a+b|2=|a|+2a.b+|b|2  b) show that…

A: Vectors a and b are two vectors. We have to answer the following...

Q: 2. Let a, b, c, and d be algebraic vectors in R3, For parts (a) and (b) below, state which theorems…

A: The dot product of the two vectors A→ and B→ is given by the following: A→·B→=||A→||·||B→||·cos θ…

Q: If are arbitrary vectors in R2x2, then the mapping A = (A, B) || A|| = ||B| = [a11 a12] a21 a22 A =…

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Q: Let P, is the vector space of polynomials of the degrees2.Use coordinate vectors to that the…

A: The main objective is to check {p1,p2,p3} linear independent and basis of P2.

Q: Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that…

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

A: Given complex numbers are z1=2+3i    and    z2 =1-2i and   given vector space  is   ℂ over ℝ

Q: Prove that if IS or thogonal to both WaXhen is orthe gonal to every it' vector 1> 1X

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