Consider the matrix -() 1 2 3 2 1 1 0 3 h A = which is the standard matrix representation of a linear transformation T. (i) Determine the explicit form of T, i.e. the formula for T(x) for any x in its domain. (ii) What is the domain, codomain, and range of T? (iii) Determine the value(s) of h such that there exists a b in the codomain of T that is not the image of some x in the domain of T. (iv) Determine the value(s) of h such that for any b in the range of T, there exists a unique x in the domain of T that gets mapped to b.
Consider the matrix -() 1 2 3 2 1 1 0 3 h A = which is the standard matrix representation of a linear transformation T. (i) Determine the explicit form of T, i.e. the formula for T(x) for any x in its domain. (ii) What is the domain, codomain, and range of T? (iii) Determine the value(s) of h such that there exists a b in the codomain of T that is not the image of some x in the domain of T. (iv) Determine the value(s) of h such that for any b in the range of T, there exists a unique x in the domain of T that gets mapped to b.
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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. The two problems I really care about ar iii and iv, since I beleive I have i and ii finished. I have no clue how to interperet part iii and part iv, however, if they are necessary for you to find the two last question, may you please offer those as well. Thank you very much
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