on , (R) defined asFind the matrices of the linear transformation TI (a, b, c) = (2b + c, a – 4b, 3a) with respect to the bases B, B' where{(1, 0, 0), (0, 1, 0), (0, 0, 1)}, B' = {(1, 1, 1), (1, 1, 0), (1, 0, G i.%3D%3D9.

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Answered: Find the matrices of the linear…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3}is a basis for ℝ^3. Also, let T: ℝ^3 → ℝ^2 be the linear map for whichT(v1) = (1,0), T(v2) = (−1,1), T(v3) = (0,1). Then find T(7,13,7)
The standard matrix of the transformation T defined by T(x,,x2,x3)= (x,+2x2,-X3 , 4x, -X3) 1 2 0 -2 0 1 0 4 1 1 2 0 0 0 -1 40 1 1201 0 4 1 40 1 1 2 0 0 0 -1 40 -1 1 2 0 20 -1 14 -1 none
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Find the standard matrices A and A' for T = T₂ o T₁ and T' = T₁0 T₂. T₁: R² R², T₁(x, y) = (x - 3y, 3x + 3y) T₂: R² → R², T₂(x, y) = (y, 0) A = A' = ↓ ↑ 00
Let T be a linear operator defined on P3 by T(a0+a1x+a2x^2)=a0+a1(x-1)+a2(x-1)^2. The third row of the matrix associated with T with respect to base 1, x, x^2 is: a) (0,0,1) b) other response c) (1,-2,1) d) (1,0,0) e) (-1,1,0)
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Let T:V → V be the transformation whose matrix relative to basis {b1, b2, b3} is Гх 3 -5 [T]B = ly 7 and T(b1 – 3b3) = 11b1 – 2b2 then [T(b1)]B %3D 2 -3 1 (a) -2 (b) -3 (c) -2 (d) 2 1 a e. None of these O b
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Find the matrices of the linear transformation T T (a, b, c) = (2b+ c, a – 4b, 3a) with respect to B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}, B' = {(1, 1, 1), (1, 1, 0), (1, 0, G i. A on (R) defined as the bases B, B' where %3D