1 C: An example of diagonalisation: Let T be the operator of C3 with matrix M = 0 0 2) Find the matrix of T in the basis (e₁, €2, €3). 1+i 2i 1 2 i 0 -i

Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = (0.375,…

A: Given: In this problem, the given details are We want to create a matrix that reflects around a line…

Q: The set is a basis for R2. Find the coordinates of the vector [x] B = = -16 11 B -6 = -{[1].[:]}…

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

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Q: Find the change of basis matrix [] and use it to find [v]• B -17] 2 0 --{@@@}-E -2 4 4 B 1 2 = -71…

A: Given Information: and To find: and Notation used: denotes the change of standard basis matrix with…

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Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = { (9, −3, 15, 4), (−3, 0, 0,…

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Q: Let A = P = [-25 4 -19 4 4 8 4 8 . Find an orthogonal matrix P with rational entries and a diagonal…

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Q: Consider the matrix A = ГО 1 1 1 1 1 1 1 0. a.) Write A-¹ as a product of elementary matrices with A…

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

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Q: For the matrix A, find an orthogonal matrix P such that P-1 A Pis diagonal. 3-2 41 A = I ده است مراد…

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Q: Results for this submission J At least one of the answers above is NOT correct. T(6₂) = 86₁ +26₂. )…

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Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: a b c] Find a, b, c, d, e, f, and g, so the matrix A = d e f 1 g rows and columns of A are…

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Q: B1 Be ß1 and B2, bases of R´, and denote by [1] the base B2 change matrix B1 to the base B2 . Given…

A: Given that the change of the basis matrix is Iβ1β2=5-2-21 Also the coordinates of the vector with…

Q: Find the change of basis matrix [] and use it to find [v].Ⓡ. B B 0 {Q[C])} 4 [V] B 0.5 -0.5 1.5 1 16…

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 7 4 2 9 +X3 +x2 HOO -9 9…

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Q: Explain why S is not a basis for P,. .2 S = (1 - x, 1 - x², -1 – 8x + 9x²} O s is linearly…

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Q: Find the standard matrices A and A' for T - T T, and T-T T3: T: R2 - R2, T,(x, y) - (x - 4y, Sx +…

A: T1(x,y)=x-4y, 5x+4yT2(x,y)=y,0T=T2∘T1 and T'=T1∘T2

Q: []B = Find the coordinate vector of = 2 4 with respect to the basis B = [1] 0 {CC)6]} 2 for R³.

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 1 +23 + Z4 [HDHIHOI…

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Q: Give a basis for the image of the matrix A. 0 0 1 -2 A = 1 -1 2 −5 0 0 5 -10 Number of Vectors: 1…

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Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2

Q: Determine the change of coordinate matrix from the given ordered basis ? to the given ordered basis…

A: Given: Given ordered basis for ℝ2 is X=-5,-3,4,28Y=6,2,1,-1 we want to find change of coordinate…

Q: Consider the following matrices: 1 0 1 4 3 1 1 2 -- %3D B = 0 1 1. [1 0 C = 0 1 -1 a) Find BC. b)…

A: If determinant of a matrix is non zero then it is invertible. Two matrix will add or subtract only…

Q: 1 Let P-3 -5 6 4 1 5 9 4 2 and V3 = 5 Complete parts (a) and (b). a. Find a basis {u₁, U₂, U3} for…

A: Transition matrix from basis B to C is related as below C=PC←BB

Q: For the matrix A, find an orthogonal matrix P such that P-'APis diagonal. 3 00 A =| 0 2 2 0 2 5

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Q: Let ß=4 [³][3] and and = are bases for R² -3 a. Find the change-of-coordinates matrix from top. 3 b.…

A: We can write the matrix form of the basis β as A=-34-10 and the matrix form of the basis ξ is…