Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0, 3, 0]) of R^3.

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: Determine whether the vector {6,1,–6, 2} is in the vector space generated by the basis vectors {1,1,…

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Q: Find the stable vector of 1 2 1 3 2 3

A: ANSWER:

Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

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Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find an orthogonal basis for A1, A2, A3 (i.e., find 3 mutually perpendicular vectors u1, u2, u3 with…

A: The solution are next step

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: Find a vector in 3d space whose magnitude is 4 and whose components have the largest possible sum

A: Find a vector in 3D space whose magnitude is 4 and whose components have the largest possible sum.…

Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

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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: Find a basis for R2 that includes the vector (2, 2).

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Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

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Q: Find a vector orthogonal to both and

A: Given query is to find the vector orthogonal to the given vectors.

Q: (0,0, 1), (0, 1, -1)} be a basis of R, Find the matrix for T relative to

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Q: orthonormal

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Q: Find a basis for R3 that includes the vectors (1, 0, 2) and (0, 1, 1).

A: Given vectors 1,0,2 , 0,1,1IR3 is a vector space of dimension 3 Let , the standard basis for IR3is…

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Do the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R²?

A: Given data:- Vector, v1=-3,7 and v2=5,5

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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Q: Does the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R2?

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Q: What are the spline basis functions for a cubic spline basis with 3 knots at values x1, x2, and x3?

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Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Find the coordinates of x = {-10, 2, 4} with respect to the basis consisting of u, {1, 3, 2}, u, =…

A: Find {a, b, c}.

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: Find the stable vector of

A: Given information: In the given Markov model, there are 2 states. A state transition matrix consists…

Q: Find a subset of vectors v1 = (1,0,1,1), v2 = (-3,3,7,1), v3 = (-1,3,9,3) and v4 = (-5,3,5, –1) that…

A: To find subset of vectors that forms a basis for the space spanned by the vectors. Form a matrix:…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0