Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31 [34] -8 96 95

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

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Q: Let a = (0, 2) and b = (- 5, 1). %3D %3D | Find the angle between the vector, in degrees.

A: Given vectors are: a→=0, 2 and b→=-5, 1

Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: Find (2x + 5y)dA where Ris the parallelogram with vertices (0,0), (-5,4), (-2,-1), and (-7,3). Use…

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Q: Find the cross product a × b. a = (6, 5, -4), b =(2, -1, 1) Verify that it is orthogonal to both a…

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

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Q: A tank contains 420 liters of fluid in which 40 grams of salt is dissolved. Pure water is then…

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Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: а. х %3 (3, —4,0, у b. х %3D (2, 1, —3, 4y c. x = (sen k, cos k, 24y para un entero positivo fijok

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: Find the matrix of the reflection about the line L.

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Q: Find the dot product of ū = (3,-2) and v = (5,-7). Select one: -1 V29 29 (8,-9)

A: Consider the vectors u→=3,−2v→=5,−7

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.