3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x, x+4x2, 5+ 6x + 3x2, 7+2x-x²

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A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

Q: Set û= and w= Write as a linear combination of these two vectors For the toolbar, press ALT+F10 (PC)…

A: HHere C1 nad C2 are scalars

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Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

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

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Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

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Q: is the sum of 2 vectors with components and . What is a?

A: To find the value of a, you can use the properties of vector addition.Given that the sum of the…

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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…

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Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: 98. Determine whether the vectors AB and PQ are B(-2, 2, 0), where A(1, 4, 1), equivalent, P(2, 5,…

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Q: Let vi = (-9,9, 6). v2 = (2, 6, 4). v3 = (4,0,0) in Rº. Find a nontrivial linear relation among…

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Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

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Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

Q: 9. Explain why four vectors is R³ are always linearly dependent.

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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.

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A: The given vectors are .We have to check whether the vectors are linearly independent or not and find…

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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