Exercise 5.8.2 Let B = in R². Find CB(x). {[+][6][+])} 0 be a basis of R³ and let x = 5 -1 4 be a vector

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Q: Let B= = (1, +2, (x - 1)², 42³) be an ordered basis for P3. Find the coordinate vector of f(x) = 1x³…

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Q: Let ^= [1] -6 Find a unit vector x whose first component is positive at which Ax has maximum length.…

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Q: Find an orthogonal basis of R4, containing vector [1, 1, 1, 1].

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Q: 5. W is spanned by the vectors 24 -3 9 and Find a basis for W¹.

A: The basis for W is:Basis of W= 24-3-8 ,  -1-225

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

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Q: Find an orthonormal basis of the plane z1 + 7z2 - 13 = 0. {

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Q: Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector…

A: To solve the following, we use the standered result of basis and spanning set Basis- Let V is any…

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find a basis for the set of vectors in ℝ2 on the line y = 5x.

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Q: Find a basis of R that contains the vectors X = (1,1,1,1) and Y = (1,1,0,1).

A: Given Vectors X =(1,1,1,1) and Y = (1,1,0,1) Now determine the orthogonal basis for R4

Q: E Let z = 1+ i and z'=i-1. 1) Are these two complex numbers independant in the real vector space C?

A: We checked two complex numbers independant in the real vector space C?

Q: {} Find in R² whose coordinate vector relative to the basis B is [x]B Let B = x = 12 -5 -6 [:] 5

A: Introduction: The coordinate vector of an element of vector space related to basis is the vector…

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: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

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Q: E Let p 8x + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, Pi = 1,…

A: We have to find the coordinate vector of P.

Q: Show that the set S = {(4,3, 2), (0, 3, 2), (0,0, 2)} is a basis for R* by showing that it spans R³…

A: Consider the provided question,

Q: Check whether the set V= {(2, 3), (3, 4)} is basis of R2 or  not?

A: this a spanning set and linearly independent so the vectors forms a basis of R^2

Q: 2. Find a basis for the set of vectors in R2 on the line y = 5x.

A: Now here,

Q: 2- Show whether the set of vectors S={ ,,} is a basis of R3 ?

A: Given the set of vectorsS={<3,2,2>,<−1,2,1>,<0,1,0>}

Q: Explain how fixing a basis v1, , Vn of V associates to a quadratic form a corresponding function in…

A: To explain how a basis v1,v2,...,vn associates to a quadratic form of a corresponding function in n…