7. fast please Thank you. 7. Consider the transformation TR4 R4 defined byT(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4)(a) Find the associated matrix for T.(b) Find a basis for ker(T).(c) Find a basis for R(T) (Range).(d) Is T one-to-one? Why?(e) Is T onto? Why?

A. 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1B.x1=x2=x3=x4=0C.{(1, 1, 1, 1), (0,…

Answered: 7. Consider the transformation TR4 R4…

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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7. Consider the transformation TR4 R4 defined by T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T one-to-one? Why? (e) Is T onto? Why?