In each part, determine whether the vectors are linearly independent or are linearly dependent in P2. (a) 4 – x+ 4x2,4 + 2x + 2x²,4 + 6x – 4x?

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: = Let -3 -1 -~--~--~--~--~- , V3 -5 1 , V₂ 2 0 combination of V₁, V2 and V3. 5 -26 , V4 -9 -1 -3…

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Q: ..... A= -1 1 is diagonalizable. Select one: True False

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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: Use the vector w= (20, -15) ||w||-19 ||w||-19=

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Q: (b) Write the following vectors as linear combinations of 21, 22, and 23.

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Q: For any two non-zero, non-parallel vectors ā and b, the vectors ā x b and (2ā + b) x (ā – b) are…

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Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

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Q: c) x = x1 – x2, x, = 5x1 – 3x2 %3D

A: To solve the given system of differential equations, first we find the eigenvalues and corresponding…

Q: For two vectors A and B, what is the value of A X B²+ (A.B)²?

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Q: Find the length of each vector.

A: Solution: Consider the given vectors are  (a) u = 0-20 The length of the vector a→ = a1a2a3  ⇒ ∥a→∥…

Q: et V₁ = (1, -2,-2), V₂ = (0, -1, -2), V3 = (2, -4,-5). re the vectors 1, 2 and 3 linearly…

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Q: determine the solution set of the linear system: x3-x4=-2 x1-x2+2x4=1 -3x1+3x2+2x3-8x4=-7 write your…

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Q: 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in…

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Q: Let u = 4u + 5v (9, -2, -8) and v = (4, −3, −1).

A: The required solution is:<56,-23,-37>Explanation:

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: x - 5x², Let v₁ = 9 + 6x², v₂ = 2 - − - V3 = 3 + x − 7x². Determine whether these three vectors are…

A: Vectors v1=9+6x2,v2=2-x-5x2,v3=3+x-7x2. The objective is to determine whether these vectors are…

Q: Write b as a linear combination of the vectors v1, v2, and v3,  where: (view attachment)   Set up…

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Q: solve using the concept of rank.

A: Given set of vectors is: S = {[4     1     2], [2      5      -5], [2      -1        3]} We have to…

Q: Calculate v × w, where v = (−2, 1, 4) and w = (3, 2, 5).

A: Given: v = (−2, 1, 4) and w = (3, 2, 5)

Q: Sketch v = (−2, 1), w = (2, 2), v + 2w, v − 2w.

A: Given vector, v = (−2, 1), w = (2, 2)

Q: Let n and r be integers such that n > 0 and 0 ≤ r ≤n. Prove that (²) ₁ = n (²-1) by counting in two…

A: Given, n and r be integers such that n>0 and 0<r<n.

Q: Given the following vectors A = -4a +3a-2a₂ X y B=a_+5a +7a_ X y z C=-2a-4a +6а X y Evaluate |AX…

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