Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector orthogonal to W. 1 HHO 8 3 -2 y= -6 7 7 The sum is y = y +z, where y= (Simplify your answers.) -2 is in W and Z = is orthogonal to W.

Q: Let u4 be a linear combination of {u₁, U₂, U3}. Select the best statement. OA. {U₁, U₂, U3, U4}…

A: Given that, be a linear combination of .The aim is to find the correct statement about the given…

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: 1 Y

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Q: Determine a so that the vector u= "- [3] is a linear combination u = av+bw of vectors *-[2]· *-6). =…

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Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: 5. Let S = {V₁, V2,..., Un}, n ≥ 2 be a set of nonzero vectors of V. Each of the following…

A: Given,  S= { v1 , v2 , v3 , ...... ,vn } , n>=2 is a set of nonzero vectors of V .

Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

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Q: 3 Determine whether the vector w = | 10 is a linear combination of the vectors v1 = 0 , v2 = -2 -3…

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Determine the dimension of the vector space. R9

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Q: what are the endpoints of vector v - u?

A: v = (-6,-7)u = (1,-3)

Q: Mr. and Mrs. Wang want to buy a house that costs $745,000. They plan to put 20% down. They are…

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Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

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Q: Use the given vectors to compute u + v, u − v, and 5u − 3v. u = (5, −2),    v = (7, 6)

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: Express v = (-i, 2 + i, -1) as a linear combination of the following basis vectors given below.…

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Q: 1 -3 8. Let vi V2 and v3 = be given vectors in R4. Which of the following vectors is a linear…

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Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. [:][ N 4 9…

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Q: 21 -2 and y -3 3 Express the vector v as a linear combination of a -4 y.

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Q: 5. v₁ = (1, 0, 0), V₂ = (0, -2, 0), V3 = (0, 0, 3)

A: The given vectors are as follows:To Find:whether the given vectors u and v are linearly dependent or…

Q: 5. Which of the following sets of vectors in P2 is linearly dependent? A. {1,x, x²} B. {1+x,1 – x,2}…

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Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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