Suppose that V = R³ and x is the following. If [x] B X = 1 0 -(ABB) 2 4 1 is an ordered basis for V, find [x], the coordinates of vector x with respect to the ordered basis B. = 9 24 3 B = 1 0

Q: 1. Determine whether the following vectors form a basis for R. -2 11

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Q: 2.Show that the following Vectors form a Wasis tor Pg. 4.ct-11.(t-1",(t-1'

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A: Given That :  Vectors in R5 are  v1=5127-7-11 , v2=102414-14-22 , v3=76-11-13 , v4=-3-30-1-5 ,…

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

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Q: The set B = • {1+t², −t+t², 1 + 2t+t²} is a basis for P₂. Find the coordinate vector of p(t) =…

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Q: Find the new coordinate vector for the vector x after performing the specified change of basis. 6)…

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A: NOTE: Refresh your page if you can't see any equations. . . write both basis vectors in the matrix…

Q: -{{}")} B = 4 -10 is a basis for R². Find the coordinates of the vector x relative to the basis B.…

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Q: Q#5: If Bij = €ijkak, show that B is antisymmetirc. %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The set B is a basis for R². Find the coordinates of the vector [Z] B 9. -10] relative to the basis…

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A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

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Q: You are given the following vectors in terms of their components in the i, j, k basis: A=11+2j+-1k B…

A: Since you have posted a multi subparts question according to guidelines I will solve…

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Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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Q: Consider the coordinate vectors -3, [als [B]s= %3D 4. 6. (0) Find B if S is the basis in: : 3 3 -12…

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A: Since  in the usual basis  has coordinates, . So, to obtain its coordinates in the basis,  , where

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Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form…

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

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A: We have to find the basis  B

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A: Vβ​=[−3​0​−2​]   Explanation:

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, − 2 + 4t², and − 12t+8t³; and…

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Q: Let W = span{(1,1,-1), (2,3,1), (5,6, -2)}. i Find a basis for W. ii. Determine whether the vector X…

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