Consider the transformation T : R4 → R3 defined by T(x1, x2, x3, x4)=(2x1 + x2 + x3 − 4x4, 6x1 − 9x3 + 9x4, 4x1 + x2 − 2x3 − 3x4) (a) Find the matrix associated with this transformation. (b) Find a basis for ker(T). (c) Is T one-to-one? Why?

Consider the transformation T : R4 → R3 defined by T(x1, x2, x3, x4)=(2x1 + x2 + x3 − 4x4, 6x1 − 9x3 + 9x4, 4x1 + x2 − 2x3 − 3x4) (a) Find the matrix associated with this transformation. (b) Find a basis for ker(T). (c) Is T one-to-one? Why?

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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Question

Consider the transformation T : R4 → R3 defined by
T(x1, x2, x3, x4)=(2x1 + x2 + x3 − 4x4, 6x1 − 9x3 + 9x4, 4x1 + x2 − 2x3 − 3x4)

(a) Find the matrix associated with this transformation.

(b) Find a basis for ker(T).

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Step 2: Find associated matrix

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Step 3: Apply elementary row operations

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Step 4: Find basis for ker(T)

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