Define T: R²R² by Tix) - Ax, where A is the matrix defined below. Find the requested basis B for R2 and the corresponding B- matrix for T. Find a basis B for Rand the B-matrix D for T with the property that D is an upper triangular matrix. A-54-400 9 08-0-3 D- OB- 0-B-1 D. OB- ----61 D= 0-1 D 0-6

Q: {[:} Given that B and C = are both bases of R², find the coordinates change matrix when we change…

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Q: Q: Determine if the following system is consistant q using matrix ? X2 - 4X3 2X1 -3X2 +2X3 =l 5x,…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

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Q: A is a 4 by 4 matrix with 1 's on the diagonal and -a, -b, -c on the diagonal above. Find A - 1 for…

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Q: Find the LU factorization of -1 -5 -4 A = -5 -26 -18 That is, write A = LU where L is a lower…

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Q: , find the change-of-coordinates matrix from the basis B= {1– 2t +t?,3 - 5t + 41,2- 2t + 5t?} to the…

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Q: Find the LU factorization of A = A = 9- -4 E -4 That is, write A = LU where L is a lower triangular…

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Q: Find the value of the vector product XY using the matrices below where p = 9 and q = 6: X = p -1 q…

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Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: In P2, find the change-of-coordinates matrix from the basis B = {1 – 3t2, 2+t – 5t², 1 + 2t} to the…

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Q: LOT A = [ ₁ - 10 Let 1 D= 0 1 1 -1 1 Construct a 4x2 matrix D, using only 1 and 0 as entries, such…

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Q: Given basis = {QOB]} {[ 2 5 3 {C₁, C2, C3}. find the basis C = of R³ and change of basis matrix [B]C…

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Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Find the LU factorization of 5 3 A = -15 -5 -5 1 That is, write A = LU where L is a lower triangular…

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: In P,, find the change-of-coordinates matrix from the basis B = {1-7,2 +t- 13t2,1 + 6t} to the…

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Q: Find the coordinate matrix of x in Rn relative to the standard basis.x = (−6, 12, −4, 9, −8)

A: The given vector is x =  (−6, 12, −4, 9, −8).One has to find the coordinate matrix of x relative to…

Q: Let B1 = {T1,t2, t 3} and C, = {w1, w2, w3} be two bases for R³ such that । = - , के = - े;, के; =…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R². B= 6 -3 9

A: The given basis B=6-3, 19. To find the change of coordinates matrix from B to the standard basis.

Q: 10. B =

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Q: The matrix A(4x3) = 3,-5,1 second row 1,1,1 third row -1,5,-2 fourth row 3,-7,8. Use the…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

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Q: Find the change of basis matrix from B₁ to B₂. B₁ = OLD 0 -8 eBook 4 B₂ = 2 -3 -1 3 7 4 (HH) -2 2 -8

A: The given bases  B1 and  B2  are ,   B1 =  542 ,    8   0-8  , -3   3   2    and             B2 =…

Q: - Create a table that counts from 0-100 in intervals of 18. - Look at the tensor below 29 0 -51] G 0…

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: In P,, find the change-of-coordinates matrix from the basis B = {1+3r²,2+t+7t?,1- 41} to the…

A: Given that                          B={1+3t2,2+t+7t2,1-4t} is a basis for ℙ2. To find the change of…

Q: 4 Compute x using the vectors w = -2 and x = (Simplify your answer. Type an integer or simplified…

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Q: In P2, find the change-of-coordinates matrix from the basis B= {1 − 2t + 1²,3 −5t + 4t²,2 − 2t +…

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Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

A: Given A=−2−26425−15−10−63−13−14−2−144635. Find the LDU factorization of A.