In Exercises 5-8, find the coordinate vector [x] of x relative to the given basis B = {b₁,..., bn}. 5. b₁ = A], b2 = 2 " X = -2

Q: Write the vector v = B - - -3 8 5 -44] 50 24 1 - as a coordinate vector with respect to the basis

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Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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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 v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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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: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Represent the vector with respect to each of the two bases { ] y = B = B2 =

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Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

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Q: (1) Show clearly the equation that you need to set up to explicitly test span (try to build the…

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Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: 2. In each question, explain the reason. Consider the following vectors in R³: (a) (b) v₁ = (1, 0,…

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Q: Assuming a vector a(2,1,3) and a vector b(-1,2,2) Length vectors Calculate 2a-b and a + 3b.

A: In this question we will use basic of vector addition, subtraction and Multiplication.  First we…

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

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

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: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

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Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: The coordinate vector of the vector (-4,3,1) in the basis B={u= (1,1,1); v = (1,0,1); w= (0,0,1) }…

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Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…