If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not possible, state the reason for that. a) w = (1,1,5), v₁ = (7,7,7), v₂ = (2,5, 3), v3 = (4,1,-1) b) w = (2,-3,2,-3), v₁ = (1,0,0,3), v₂ = (0,1, -2,0), v3 = (0,-1,1,1)

Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

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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: If possible, find a linear combination of the form w = a₁v₁ + a₂V₂ + a3V3 where v₁ = (2, -1, 4), V₂…

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Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

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Q: Suppose that v₁ = (4, 4, 0, 7), v₂ = (2, -5, 5, 4) and v3 = (-7, 0, 5, 2). Is the following vector…

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Q: Let -BHGH) V₁ If possible, express was a linear combination of the vectors ₁ and ₂2. Otherwise,…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given : The given set is  S = {(2, -1, 3) , (5, 0, 4)}. To find : We have to write the following…

Q: 1 V₁ = 2 - Copyright Texas State University, 2 3 rights reserved. V₂ = University, 2023 1 1 V3 =…

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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Q: f possible express the vector v as a linear combination of 1, V2, and V3. b) v = (0, 0, -1), V₁ =…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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

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

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Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

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Q: (1) S={(2,-1,3), (5,0,4)} (a) u=(1,1,-1) (b) w=(1,-8,12)

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