Let W be the subspace of R5 spanned by the vectors = (1,2,3,1,2) and v= (2,4,7,2, -1). A basis of the orthogonal complement W of W is ... OA. {(1,2,3,-1,2), (2,4,7,2,1), (2, - 1,0,0,0) } O B. ((-17,0,5,0,1), (13,0, -4,1,0), (2,-1,0,0,0) } C. None in the given list OD. {(2,-1,0,0,0), (13,0,- 4,1,0), (1,0,0,0,0) } O E. {(1,0,0,0,0), (0,1,0,0,0). (0,0,1,0,0) }

Q: Determine whether or not the given vectors form a basis of R4 V1 %3D (-2, 6, 2, 4), v2 3D (1,0,…

A: To Determine: whether or not the given vectors form a basis of R4 Given: we have  v1=-2,6,2,4…

Q: 7. v₁ = (0, 0, 1), V2 (0, 0, 1), V₂ = (7, 4, 11), V3 = (5, 3, 13) 8. V₁ = V1 (2, 0, 0, 0), v₂ = (0,…

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Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

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Q: Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector…

A: To solve the following, we use the standered result of basis and spanning set Basis- Let V is any…

Q: Let W be the subspace spanned by the vectors (1,2, 0, 3) and (2, 1,3,0). Find : a basis for W+.

A: Given that W is a subspace spanned by the vectors 1 , 2 , 0 , 3 and 2 , 1 , 3 , 0 . i.e., W = span1…

Q: Let V be the subspace of R' spanned by the vectors below: u = (1,2, 1,3,2), Uz = (1,3, 3,5, 3), Uz =…

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Q: Verify that the vectors (1,0,1), (1,1,-1), es= e₂ = form an orthonormal basis (ONB), and compute the…

A: Given vectors are  .We have to show that these form a orthonormal basis for inner product space…

Q: or the given sets of vectors, find the dimension of the space spanned by them and basis for this…

A: In this question, we will find the dimension and basis of space.

Q: Let W be the subspace of R³ spanned by the vectors =(1,2,3,-1.2) and v= (2,4.7.2.-1). A basis of the…

A: Let W be a subspace of a vector space V. Then orthogonal complement of W is defined as, W⊥={u| v∈W…

Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Find a basis of R that contains the vectors X = (1,1,1,1) and Y = (1,1,0,1).

A: Given Vectors X =(1,1,1,1) and Y = (1,1,0,1) Now determine the orthogonal basis for R4

Q: Find a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors.…

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Q: Find a basis for the subspace of R'consists of all vectors of the form (a, 2a + b, b, 0). State its…

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Q: Let W be the subspace of RS spanned by the vectors = (1,2,3,-1,2) and v= (2,4,7,2,-1). A basis of…

A: We have to solve given problem:

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 16.- Obtain a…

A: Given vectors are a=(1,3,-1), b=(-2,1,3), c=(3,2,1), and d=(1,-1,2).

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

A: We have to find a basis for the subspace of R³ that is spanned by the given vectors.

Q: Find the terminal point Q of the vector v = 7i-j+3k given the initial point is P(-2, 3, 5) О (5, 2,…

A: In this question we have to find the terminal point of Q.

Q: Find a basis for the subspace of R³ that is spanned by the vectors V₁ = (1,0,0), v₂ = (1, 1, 0), v3…

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Q: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

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Q: The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w=(0,0,1) }…

A: We have to find the coordinate vector of the vector -4, 3, 1 in the basis B=u=1,1,1; v=1,0,1;…

Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: Let V₁ = (1,4,5,6,9), v₂ =(3, 2, 1,4, -1), V3 = (-1,0,-1, -2, -1), V4=(2,3,5,7,8), Find a basis for…

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Q: S= {(1,1,1), (1,2,-3), (5,-4,-1)} is a set in R'. Show that a) Sis orthogonal. b) Write w = (1, 5,…

A: Orthogonal set is the set in which dot product of two vectors is zero.