A transformation $ T $ is defined by $ T(\vec{x}) = A\vec{x} $.The matrix $ A = \begin{bmatrix} 0 & -12 & 3 & 2 \\ -4 & 0 & -6 & 2 \\ 0 & -15 & 3 & 3 \end{bmatrix} $ reduces to $ \begin{bmatrix} 4 & 0 & 0 & 2 \\ 0 & -3 & 0 & 1 \\ 0 & 0 & -3 & 2 \end{bmatrix} $.Find a basis for the kernel of $ T $:[Input box 1][Input box 2][Input box 3][Input box 4][Calculator button] [Check Answer button]

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Answered: A transformation I' is defined by 1'(x)…

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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A transformation I' is defined by 1'(x) = Ax 0-12 -12 3 3 2 -6 2 3 The matrix A= -4 0 0 - 15 3 Find a basis for the kernel of T: A reduces to 4 0 0-3 0 2 0 0 1 0 0-3 2