a) Let T : R* → R³ be a linear transformation such that for any y e R thereare infinitely many a € R' such that T(x) = y. Write down a matrix in echelonform which could be the standard matrix of T. Explain why your matrix works.b) Let T: R → Rª be a linear transformation such that if y e Range(T) thenthere is a unique x € R such that y = T(x). Write down a matrix in echelonform which could be the standard matrix of T. Explain why your matrix works.

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a) Let T : R* → R³ be a linear transformation such that for any y e R there are infinitely many a € R' such that T(x) = y. Write down a matrix in echelon form which could be the standard matrix of T. Explain why your matrix works. b) Let T : R³ → R“ be a linear transformation such that if y E Range(T) then there is a unique æ e R such that y = T(x). Write down a matrix in echelon form which could be the standard matrix of T. Explain why your matrix works.

a) Let T : R* → R³ be a linear transformation such that for any y e R there are infinitely many a € R' such that T(x) = y. Write down a matrix in echelon form which could be the standard matrix of T. Explain why your matrix works. b) Let T : R³ → R“ be a linear transformation such that if y E Range(T) then there is a unique æ e R such that y = T(x). Write down a matrix in echelon form which could be the standard matrix of T. Explain why your matrix works.

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

a) Let T : R* → R³ be a linear transformation such that for any y e R there
are infinitely many a € R' such that T(x) = y. Write down a matrix in echelon
form which could be the standard matrix of T. Explain why your matrix works.
b) Let T: R → Rª be a linear transformation such that if y e Range(T) then
there is a unique x € R such that y = T(x). Write down a matrix in echelon
form which could be the standard matrix of T. Explain why your matrix works.

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