lo nierob xiv) Is T onto? Explain your reasoning. noto xv) Find a basis for the kernel of T. Twi lo ooiensil xvi) Is T one-to-one? Explain your reasoning.

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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14,15,16
2. Let T be the transformation T(x, y, z) = (x- 2z, 2y + x, x +3z) ni oolm
vig tonnao 1 a
xi)
Determine the domain of T.
xii)
Determine the codomain of T.
xiii)
Find a basis for the range of T.
g tadi xitemm ol bei
Tlo nietob di snimt
хiv)
Is T onto? Explain your reasoning.
xv)
Find a basis for the kernel of T.
l to coiensmib od stusis
Ceum i rand a bri1
xvi)
Is T one-to-one? Explain your reasoning.
ed io coienonib odi onitms
Is T an isomorphism? Explain your reasoning. If it is, write the inverse
transformation. (Don't just give the inverse matrix! I want the inverse
TRANSFORMATION!)
xvii)
xviii) Prove that T is a linear transformation. (Do this on a separate piece of paper.)
he rai ton
Transcribed Image Text:2. Let T be the transformation T(x, y, z) = (x- 2z, 2y + x, x +3z) ni oolm vig tonnao 1 a xi) Determine the domain of T. xii) Determine the codomain of T. xiii) Find a basis for the range of T. g tadi xitemm ol bei Tlo nietob di snimt хiv) Is T onto? Explain your reasoning. xv) Find a basis for the kernel of T. l to coiensmib od stusis Ceum i rand a bri1 xvi) Is T one-to-one? Explain your reasoning. ed io coienonib odi onitms Is T an isomorphism? Explain your reasoning. If it is, write the inverse transformation. (Don't just give the inverse matrix! I want the inverse TRANSFORMATION!) xvii) xviii) Prove that T is a linear transformation. (Do this on a separate piece of paper.) he rai ton
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