Suppose that you wish to find the projection of u = (3,0,6)" onto the subspace W of R spanned by (2, 1,0)" and (0,1,-1). 'Set up the normal cquations for this problem. Use the normal equations to find the projection of u onto W. (a)

Q: Show that [0, ∞) and (0, 0) ad subspaces of R with the usual topology are not homeomorphic.

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Q: 1. Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices? Support your…

A: I have showed that any two vectors form W linear combination of these also lies on W

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A: The given equation is the parabolic equation                    y = x2

Q: Is the union of two subspaces of a vector space, a subspace.

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Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Let v1=[ 1 0 −1 ], v2=[ 2 1

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Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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Q: Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R spanned by V1 = (1,…

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Q: Find the standard matrix for the orthogonal projection of R3 onto the subspace spanned by aj=(1,1)…

A: The vectors that span the subspace are a1=1, 1 and a2=0, 1. The normalising vectors are 12, 12 and…

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: Find the orthogonal projection of 4 onto the subspace W of R* spanned by 1 1 -1 projw (7) =

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Q: Why are [0,1] and (0,1] which are subspaces of the real number system with the usual topology not…

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Q: Find the projection of the vector v onto the subspace S. 8. 4 S span 23/2 9. projs V = 11/2

A: Find the projection of vector V.

Q: |Find basis for the set of vectors in R²on the line y = nx. where n is last digit of your arid…

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Q: Find the projection of the vector v onto the subspace S. S = span

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Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

Q: what is the smallest subspace containing the vectors u, v and w? what is the span of a set of…

A: Span is the all possible linear combination

Q: Find the dimension of the subspace W of R' spanned by set S = {(-1,2,5,0), (3,0,1,–2), (–5,4,9,2)}

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

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Q: Find the distance from the point x = (1, 3, -2) of R3 to the subspace W consisting of all vectors of…

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Q: 16 In the vector space R, let u= (1, 2, 3), v -(3, 1, 5), w-(3,-4, 7). Prove that the subspace S…

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Q: Compute the normal vector to the surface Ф(и,0) %— (и? — 0?, и +0, и — 0) at that point (4,3).

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Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

A: Introduction: The Gram–Schmidt system is a way for orthonormalizing a fixed of vectors in an…

Q: Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does…

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Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: 1. Find the ortho gonal puojection of the Vector (1,3,1 on the subspace of IR? Spanned by…

A: Projection

Q: Find an orthonormal basis for the subspace W of IR* spanned by th (а) vectors (1,4, ,…

A: (a) Given that (1,4,2),(-2,-1,3) and (6,-1,-1) This can be written as, A=142-2-136-1-1 So, let's…

Q: The span of a set of vectors from a vector space V is a subspace of V. true or false?

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Q: Find the projection of the vector v onto the subspace S. 1. S = span v = projs v =

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Show that [0, 1] and (0, 1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Find the projection of the vector v onto the subspace S. S= span projs v =

A: Any linear subspace is a combination of many subspaces, these subspace may distinguish with each…

Q: Do vectors of the form {[ ]:x*+y*+z"<1} form a subspace of ie?? please explain what 37

A: The given set is                             xyz : x2+y2+z2≤1 Definition of Subspace: Let V be a…

Q: Describe explicitly a linear transformation from V, (R) into V, (R) which has its range the subspace…

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Q: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: (1, 2, 3, 4, 6) and let W be the subspace of R° spanned by {u1, u2}, where u1 (1, 2, 1, 2, 1) and uz…

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Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: 6. The projection of 12 onto the subspace of R spanned by ĝ V2 and a, 1 equals: -6 1,

A: 1. Let S be a non-trivial subspace of a vector space V and assume that v is a vector in V that does…

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: Find the orthogonal projection of 10 onto the subspace W of R° spanned by 9. and 3 -1-10 3 projw (i)…

A: To find  The orthogonal projection of v onto the subspace of W spanned by the given vectors.

Q: Find the orthogonal projection of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Q: Let ui = (1, –2, – 1), u2 = (2, 2, -2), and v = (0,0, 1). v is not in the subspace W spanned by u,…

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

A: Given:   v = 123 , u1 = 2-21 , u2 = -114    Also, given that the subspace W is spanned by the…