1. Let A=M³ (f)BBbe the matrixassociated with the linear mapf(x,y,z) = (3x − y + 4z,y + z − x,x+y+z)relativetothebasesB={u=(4,18,6), v= (17.1.0), w = (17,0,- 5) }andB'={u'=(2,2,1); v' = (1,0,0); w'=(3,2,0) }Then the first column of A is:

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Answered: 1. Let A=M³₂ (f) be the matrix B'…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let A = M (f) be the matrix associated with the linear map ƒ((x,y,z)) = (x-2y,y+z,0) relative to the bases B={u= (1,0,3); v = (0,2,1), w = (2,1,0) } and B'= {u'=(0,0,2); v' = (1,0,3); w'=(1,3,1) } Then the first column of A is: O O 1/2 - 1/2 - 1/2 1/2 -1/2 1/2 - 1/2 1/2 -1/2
Find the standard matrices A and A' for T = T₂ o T₁ and T' = T₁ 0 T₂. T₁: R² → R², T₁(x, y) = (x - 5y, 2x + 3y) T₂: R² R², T₂(x, y) = (0, x) A = Juma A' = SHE
Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1), (1, -1)} A' =
1. Let A=MB (f) be the matrix associated with the linear map f(x,y,z) = (3x-y + 4z,y+z-x,x+y+z) relative to the bases B={u=(4, 18,6), v= (17.1.0), w (17,0,-5) } and Then the first B'= {u'=(2,2,1); v' = (1,0,0); w'=(3,2,0) } column of A is: O A. 2 "B 1 3 B. - - 16 On () 13 1 C. D. E. 7 -5 3 4 17 17 3 -
Can we express the vector a = (2, – 5, 3) as a linear combination of the vectors e = (1, 1, 1), e, = (1, 2, 3) and e, = (2, – 1, 1) in R'(R). ||
6. Determine the matrix of the linear mapping defined by first mirroring the space vectors in the line with equation (x, y, z) = (2-2+, -2+2+, 1-t) and then rotating 풍 them by the angle II around the x-axis in the positive direction.
3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4
The third column of the change of basis matrix from the basis B= {u=(1,1,1) ; v= (1,0,1); w=(0,1,1 } to the basis B'= {r= (3,4,1); s= (3,0,1); t=(-4, -1, -2) is:
1. Let A = MB (f) be the matrix associated with the linear map f(x,y,z) = (2x − 2y+z, x − 4y+z, x-y-z) relative to the bases B={u=(5,16,1); v= (2, 1, –4); w=(7,17,2)} and B'={u'=(2,0,1); v' = (1,0,1); w'=(3,2,0)) Then the second column of A is: *) 0 O A. (0 O B. "B) °) SOC. O D. (6)
1. Let A = MB (f) be the matrix associated with the linear map f(x,y,z) = (3x−y+4z,y+z−x,x+y+z) relative to the bases B={u=(4,18,6), v= (17.1.0), w=(17,0,−5)} and B'={u'=(2,2,1); v'=(1,0,0); w'=(3,2,0) } Then the first column of A is: OA.-16 O B. 13 1 4 17 17 °C) O D. (2 213 O E. "G) ņ m

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1. Let A=M³₂ (f) be the matrix B' associated with the linear map f(x,y,z) = (3x − y + 4z,y+z-x,x+y+z) relative to the bases B={u=(4,18,6), v= (17.1.0), w = (17,0,- 5) } and B'={u'=(2,2, 1); v'= (1,0,0); w'=(3,2,0) } Then the first column of A is: