Let W be a subspace of R4 spanned by the set Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}. (i) Show that Q is a basis of W. (ii) Does the vector u = (-3,2,5, 5) belong to space W? If that is the case, find the coordina vector of u relative to basis Q.

Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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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: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

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: Find a basis of R3 that contains the vectors (1,0,1) and (1,-1,1)

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Prove that the vectors (1,1,0),(3,1,3) and (5,3,3)  are linearly dependent

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Q: Let W be the subspace consisting of all vectors 13 a of the form 15 a – 16 b where a and b - are…

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Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

A: We know that the dimension of vector space  is 3.If the given three vectors are linearly…

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

A: Solution is given below

Q: Let H span {(0,-1,-2), (-2, -4, 1), (3, 3, -1)}. A basis for the subspace HCR³ is { 2. }. vector

A: The basis are  { (1,-1,0) (0,-6,1) (0,0,13) and these are linearly independent vectorsExplanation:

Q: Consider the subspace S of the Euclidean inner product space R4 spanned by the vectors v₁ =…

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Q: Find a subset of vectors v1 = (1,0,1,1), v2 = (-3,3,7,1), v3 = (-1,3,9,3) and v4 = (-5,3,5, –1) that…

A: To find subset of vectors that forms a basis for the space spanned by the vectors. Form a matrix:…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Let {u, u2, u3, u4} be the orthogonal basis for R given below. Write x as a sum of two vectors vand…

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Q: Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets…

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