8. Let \( T : \mathbb{R}^3 \to \mathbb{R}^3 \) be a transformation defined by \( T(x_1, x_2, x_3) = (3x_1 + 5x_3, x_2, -x_3) \).(a) Represent \( T \) as a matrix with \( T(x) = Ax \).(b) Determine whether \( \mathbf{b} = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \) is in the \( \text{range}(T) \).

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Answered: Let T : R3 → R³ be a transformation…

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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Find the matrix A of T. A= Consider a linear transformation T from R³ to R² for which = E T = [8]. T = T * (E) - · *(8) - · *(6) - A -H). =
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f and g are linear transformations which in matrix form are (0 -4) and (3 3) (2 1) (-5 -4) What is the image of the point (-1,1) under the composite transformation g o f?
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assume that T is a linear transformation. Find a Standard matrix of T. T: IR² →IR" 8) where A T(e₁) = (5,1,5,1) T(e₂) = (-3₁7,0,0) ? e₁ = (1,0) € 2 = (0₁1) (integer or decimal)

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Let T : R3 → R³ be a transformation defined by T(x1,x2, x3) = (3x1 +5x3, x2, –x3). (a) Represent T as a matrix with T(x) = Ax. %3D (b)- Determine whether b = is in the range(T).