Answered: 4. Suppose that T : R* → R² is a linear…

4. Suppose that T : R* → R² is a linear map defined by T (x1, x2, x3, x4) = (2x1 x2 + x3, -2x1 – x2 + x3 – x4). Find the dimension of null {T}. Is T a surjective (onto) map?

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

4. Suppose that T : R* → R² is a linear map defined by
T (x1, x2, X3, X4) = (2x1
– x2 + X3, –2x1 – x2 + X3 – X4).
-
Find the dimension of null {T}. Is T a surjective (onto) map?

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