16 13 Given v = 59 find the coordinates for v in the subspace W spanned by -2 -2 -3 -1 -2 u1 = - u2 = and uz = -2 2 -14 Note that uj, uz and uz are orthogonal. v = u3 4,

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, V1 + V2,…

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Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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

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Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

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Q: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

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Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: Determine whether the vectors v₁ =(4,-8, 12), and v₂ = (-5, 10, 15) are linearly independent; if…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V, V1 + V2,…

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Q: Express the vector x as a linear combination of the u's. -17 U₁ = 0, U₂ = 5, U3 = 6, X = -43 -14…

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Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…

Q: 2. Describe the subspace of R³ (is it a line or a plane or R³?) spanned by (a) the two vectors (1,…

A: Given data:- v1, v2,v3 are vectors in R3.

Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.