Find the coordinate vector of u relative to the given orthonormal basis B. 1 2 2 2 2 1 2 1 2 и%3D (2, 4, 5); В %— | 3' 3' 3 3' 3 3'3 UB II

Q: e set B = {v= (1,1,1 a basis of R. 3. Linearly depende

A: Given set B = { v = ( 1, 1, 1 ), u = ( 0, 0, -3 ),  w = ( 2, 2, 0 ) } Then B is: -  A. a basis of R.…

Q: Find the matrix A′ for T relative to the basis B′.T: R3→R3, T(x, y, z) = (x + 3y, 3x + y, −2z), B′ =…

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Q: Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (x – y + 8z, 8x + y – z,…

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Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 2)}, x = (10, 8)…

A: If A is a basis, then x∈Rn can be written as linear combination of the elements of A. When a scalar…

Q: 5. Let V = R3 and let (, ·) be the standard dot prod- uct. (a) Calculate (3e, + 2e, – e3, 2e, +…

A: Assuming the given vectors e1, e2 and e3 are standard basis vectors. <e_i , e_j>=0 for i≠j…

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (2x - 3y, 5x), B' = {(-2,…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

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Q: [0] What values can k take for its vectors to form a basis? R3 k in space 1 2 1 O A) keR O B) k+1…

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Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

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Q: 1. Given the vectors vi = (1,2, 1), v2 = (1, 1, 1) and v3 = (1,0,0). Transform the vectors into…

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Q: Find the matrix A′ for T relative to the basis B′.T: R3→R3, T(x, y, z) = (x, y, z), B′ = {(1, 1, 0),…

A: Given transformation is

Q: Find the matrix A' for T relative to the basis B'. T: R3 R3, T(x, у, 2) %3 (у + z, х — 2, х + у), В'…

A: Given T:ℝ3→ℝ3, Tx, y, z=y+z, x-z, x+y Basis B'=5,0,-1, -3,2,-1, 4,-6,5 Let…

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(1, 2, 3), (1, 2, 0), (0, −6,…

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Q: 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the…

A: Solution :-  the given vecots are e1 = ( 1; 0; 0 )  , e2 =  ( 0; 1; 0 )  , e3 = ( 0; 0; 1 )  and  (…

Q: 4. Present the standard basis vectors e, and ez in R? as linear combinations of (3, 1) and (1, 3).

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate…

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Q: Find the matrix A' for T relative to the basis B'. T: R3 → R, T(x, y, z) = (x – y + 4z, 4x + y – z,…

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Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (5x + 4y, 4x + 5y), B′ = {(12,…

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Q: 2 3 1 0 1 1 1 1 1 1 Find the coordinate vector of A = with respect to the basis B of M22' 4 5 0 0 1

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: Let S = and T = be ordered bases for R2. Let v = and w = (a) Find the coordinate vectors of v and w…

A: Given: S=12,01 T=11,23 v=15 w=54 (a) Let v=a11+b2315=a11+b23. Then, a+2b=1 and a+3b=5, On…

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R, T(x, y) = (4x – 3y, 5x), B' = {(-2,…

A: We have to find the matrix A' for T relative to the basis B'.

Q: 3 2 2 1 a) X1= b) Уi%3D| - 3 y2=| 1 X2= 3 X3= 1 4 y3= 1 3 1 N O

A: X=x1,x2,x3 be set of vectors. Let A=x1,x2,x3 and AT=x1x2x3 G=AAT where G is dram matrix. If G is…

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R. [x] = x = (2,-1,-4), B = -…

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Q: [0.5446 and L0.8337. Find the values of y, and y2 such that vectors constitute an orthonormal basis…

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Q: the matrix of T relative to the basis B= {(1, 1), (- 1, 0)} and verify that [T], [a], = [T(a)]B Va e…

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Q: Let S = {vi, v2, v3} where v = (1,0,1), = (1,1,0) and (0,0,1) be a basis of R³. Let T = %3D %3D %3D…

A: Given: PS,T=12-111-1221S=1,0,1,1,1,0,0,0,1

Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

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

Q: (a) Find the coordinate vector of æ with respect to the ordered basis E = -2 of R3:

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Q: Find the matrix A' for T relative to the basis B'. T: R > R, Tх, у, z) %3D (у — z, х - z, х + у), В'…

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Q: Find the matrix A' for T relative to the basis B'. T: R? → R² , T(æ,y, z) = (x, y, z) B' ={(1, 1,…

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Q: Find the coordinate matrix of x in Rº relative to the basis B'. B' = {(3, 0), (0, 8)}, x = (24, 16)…

A: Given the basis B'=3,0,0,8  and x=24,16 Let x1, x2 is coordinate vector that is xB'=x1x2 Then it…

Q: Apply Gram-Schmidt orthogonalization to the column vectors of A, a1 = (1, 1, 0)T ,a2 = (1, 0, 1)T ;…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (−3x + y, 3x − y), B′ = {(1,…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(2, 0), (0, 6)}, x = (8, 30)…

A: The vector is x=(8,30) The basis is B'=2,0, 0,6.

Q: Find the matrix A' for T relative to the basis B'. T: R - R, T(x, y, z) = (x - y + 4z, 4x + y – z, x…

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Q: Define T: R-R by Tix) =Ax, where Ais the matrix defined below. Find a basis B for R? with the…

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Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(1, 0, 0), (0, 1, 0), (1, 1,…

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Q: et u be a vector in R" such that u'u = 1, and let A denote the (n x n) matrix A = --2uu". Is A…

A: We are given with multiple parts of the questions and our guideline is solve first 3 subparts so…

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + 2y, y), B' = {(-4, 1),…

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Q: Find the matrix A′ for T relative to the basis B′.T: R3→R3, T(x, y, z) = (−x, x − y, y − z),B′ =…

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Q: For the matrix below, where C', C², ..., C° denote its columns 1 2 1 3 1 4 3 8 3 15 2 A = 1 2 2 3 11…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1),…

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Q: Find the coordinate matrix of w relative to the orthonormal basis B in R". 3/34 5/34 5/34 3/34 ) (…

A: Theorem: If B = {v1, . . . , vn} is an orthogonal basis for ℝn, then the i-th coordinate of a vector…

Q: Find the coordinate matrix of w relative to the orthonormal basis B in R". {(- 5V34 3V34 3V34 5V34 w…

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Q: (1,0,0) and v = (1, 1, 1). 5. Let M (a) Find a unit vector uz E M orthogonal to e, (so that e, u2 is…

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Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 7)}, x = (40, 21)…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(5, 0), (0, 9)}, x = (40, 45)…

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