Suppose a vector y is orthogonal to vectors u and v. Show that y is orthogonal to the vector u + v. Let W = Span{v1,..., Vp}. Show that if x is orthogonal to each v;, for 1

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: (2) For every vector u and vector v in se A) True B False

A: Introduction: Vector is a quantity that has both magnitude and direction. Some mathematical…

Q: Find all values of a such that the vectors = and are perpendicular

A: Given:The vectors are  and  are perpendicular.To Find:The value of .Concept Used:When two vectors…

Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: The objective of the question is to verify if the vector w is equal to the sum of the vectors V1,…

Q: Let m (1, 2, 3) and n (5, 3,-2). Find the vector projection of m onto n, that is, find proj- m. You…

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Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: "ove that if two vectors are linearl y de pendent, e of them is a scal ar mul it ple of the other.

A: Two vectors are linearly dependent, one of them is a scalar mulitple of the other.

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Suppose that three vectors u, v, and w are linearly independent in some vector space. Are the…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given three vectors which span w.

Q: Show that the vectors 3 Ot span R³ by giving a vector not in their span. B00 4

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Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: Suppose u, v, and w are vectors in R³ and W = span{u,v,w}. Let x be a vector in R³ that is…

A: We are given that x is orthogonal to each of the vectors u, v, and w. Thus, x is orthogonal to any…

Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

A: Here, v1,v2,v3 is an orthogonal set of vectors in R5 and w is a vector in Span(v1,v2,v3) such…

Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

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Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: 6. Let a = (1, 0, 3) and u = = (2,-1,5). ) Evaluate projau. Find a vector that is orthogonal to…

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Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.

Q: Suppose that v = (v1, v2, ..., vn) and ū = (u₁, U2, ..., Un) are a pair of n-dimensional vectors.…

A: We have to define formally the predicate AlmostTheSame(v→,u→) for n dimensional vectors v→ and u→.

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: Do vectors wi = 2+ x and w2 = 3 – x, span P1(R)

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