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.

Name: . The two problems I really care about ar iii and iv, since I beleive
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Description: . 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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 33EQ

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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

Consider the matrix

\[
A = \begin{pmatrix}
1 & 2 & 3 \\
2 & 1 & 1 \\
0 & 3 & h
\end{pmatrix},
\]

which is the standard matrix representation of a linear transformation $ T $.

(i) Determine the explicit form of $ T $, i.e. the formula for $ T(\mathbf{x}) $ for any $ \mathbf{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 $ \mathbf{b} $ in the codomain of $ T $ that is not the image of some $ \mathbf{x} $ in the domain of $ T $.

(iv) Determine the value(s) of $ h $ such that for any $ \mathbf{b} $ in the range of $ T $, there exists a unique $ \mathbf{x} $ in the domain of $ T $ that gets mapped to $ \mathbf{b} $.

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