(a) Write the vector w = (1,1, 1) as a linear combination of vectors in the set S given by S = {(1,2,3), (0, 1,2), (–1,0,1)}

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Determine (if they exist) the values ​​of the parameters α and β so that the vector (4, 9, -57, 17)…

A: this is the question of vector  and here the summation of vector is given  we have to find the value…

Q: Show that vectors (86, 87, –46), (-8, –6, –2), and (-6, –7, 6) are linearly dependent-that is, there…

A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

Q: QI. Show that the vectors x, =(1,2,4), x, = (2,-1,3), x, (0,1,2) and x, =(-3,7,2) are linearly…

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Q: 1. Determine if the following vectors are linearly dependent or independent. Find an exact (non-…

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

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Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

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Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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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: Let u+ v = (3, –2) and u – v = (-4, –3). (a) Find u and v. (b) Draw the vectors u, v, – u, - v, u+v,…

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

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Q: show that the vectors V₁ = (2,0,- 2, 1) > V₂ = (3,1, -5,0) and V3=(2, 2, -6, -2) form Linearly…

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Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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

A: To find the image of v , we have to pass v to the input of T.   To find the pre-image of w, we have…