Let u, v, and w be vectors in R³. Given that v and w are linearly independent, but u, v and w are linearly dependent, what conclusions can we draw? Vectors v and w span a plane. u. (V x W) = 0. Vectors v + w and v w are linearly independent. vxw = 0. Vector u is a linear combination of v and w.

Q: Use the accompanying figure to write each vector listed as a linear combination of u and v. Vectors…

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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: Express the vector t as a linear combination of the vectors u, v, and w. 1 2 2 t = v = - 4 - 4 u= 14…

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Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

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Q: Express the vector t as a linear combination of the vectors u, v, and w. 1 - 2 4 t = 0 , u = 5 , v =…

A: We use the definition of the linear combination of vectors to answer the given question.

Q: If --0--0---0 1 and v3 = 0 then the vectors V1, V2, and v3 are linearly dependent. Select one: O…

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Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: Let W= W= , V1 = , V2 = V3 = If possible, express w as a linear combination of the vectors v₁1, V2…

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Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: Q4. Determine whether the vectors are linearly dependent or independent. v1=(4,-2, 2), v2 = (5, 4,…

A: v1=4-22, v2=54-3, v3=-793 We have to check whether the given vectors are linearly dependent or…

Q: 1. Let x = i +4j + 2k and y = i - 3j - k. In this question, write all vectors in i, j, k notation.…

A: Let (a) To find .(b) To find .(c) To find .(d) To find .

Q: Express the vector x as a linear combination of u,, u2, and uz. – 2 3 - 2 ,x = 0 u2 = 5 u3 = – 4 u1…

A: Given u1=-201, u2=356, u3=-26-4 and x=-99-38

Q: Let 52D If possible, express w as a linear combination of the vectors 71, 02 and 3. Otherwise, enter…

A: We have to write w as a linear combination of v1 , v2 and v3.

Q: Let the points A = (1, 0, 2), B = (3, 3, 1) and C = (−1, 4, 1) and the vector v = (1, 1, 3) a. Find…

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Q: Find if the vector w = (-3,2,-6) can be expressed as a linear combination of the vectors v₁ =…

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Q: a. Write the vector (8,5, 30) as a linear combination of a₁ = (4, -4,1), d₂ =(4,-5, 5) and d3 = (0,…

A: (a) Let,   <8, 5, 30> = a<4, -4, 1> + b <4, -5, 5>+ c<0, -4, -4>     =>…

Q: Assume v₁ = [3,-2] and v₂ = [-1,4]. Find the sum and difference of vectors v₁ and v₂. V₁ + V₂ = [ ]…

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Q: a. Write the vector (-4,-8,6) as a linear combination of a₁ = (1,−3,−2), ẩ₂ = (-5, -2,5) and a3 =…

A: The given vectors  and .(a) The aim is to write the vector  as a linear combination of the given…

Q: Express the indicated vector w as a linear combination of the given vectors v1 and v2 if this is…

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