11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors (2, 6, -1) and (4, 8, 3).

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: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: 1] Determine whether the first vector is a linear combination of the other vectors. (c) (-1, 15);…

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Q: 123 Write the vector 2 as a linear combination of the vectors 3 4 (6676) 5 4 2

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Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: Determine if the vectors , and are linearly independent.

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Q: Consider the vectors A= (4, -2, 2), B =-(-2,3,0), and C= (0, 2, 1). 1. Find the following. (a) B- A…

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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: 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: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: Express i = (3,7,-4) as a linear combination of i = (1,2,3), ỷ = (2,3,7), z = (3,5,6), also check…

A: see below the answers

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: Q5. Express the vector w = (1,0, −7) as a linear combination of the vectors v1=(5, 3, 4) and v2=(3,…

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Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,