et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x² + 6x − 5 relative to B. B = X -5 6.x x + 9 2+² (x-1)² 1

Q: Question 6 Let A' = [-4 16 8] and B' = [-1 x² 21 For which real value(s) of x are vectors A and B…

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Q: If vector A = [4,1] and vector B = [-3,2] and A-B = [-1,-1]  Sketch the computation above and…

A: Given; vector A = [4,1] and vector B = [-3,2]

Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Write the vector (2, –3) as a linear combination of (2, –1), (–1,2) Select one: O 2/5(2, –1) +…

A: We need to find the linear combination of the given vector. NOTE - all the options given are wrong.…

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

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

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: 3 = [ ¹₂ ], b = [ ³ ], c = [ ¹₁ ], d = [¯^¹'], and v = [¯2²], 5. Given vectors a = (a) Find all real…

A: We are given the vectors and we have to solve given problem.

Q: To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and…

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Q: Find each vector sum u + v. a. u = (1, 4), v = (2, −2) b. u = (3, −2), v = (−3, 2) c. u = (2, 1), v…

A: a). b).

Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

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: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

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Q: Find the vector x determined by the coordinate vector -[-] -{]-[G]}- XB = and the basis B =

A: To find the vector x determined by the coordinate vector  and the basis B = , we can use the…

Q: Verify the identity Ax(BXC) = B(AC) - C(A-B) using the following vectors A = ax + 2ay + 3az B = ax…

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Q: Solve for all vectors X so that × X = .

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Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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Q: Find the components of the vector - 4c based on the vector shown.

A: The magnitude of the vector in x direction is represented by i component. The magnitude of the…