**Find all the values of $ h $ (if any) for which**(a) The linear transformation $ T(x) = Ax $ is one-to-one.(b) The columns of $ A $ span $\mathbb{R}^3$.Briefly justify your answers.\[ A = \begin{bmatrix} 1 & -3 & -2 & 2 \\ 2 & -6 & -3 & 7 \\ 3 & -9 & -6 & h \end{bmatrix} \]

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Find all the values of h (if any) for which (a) The linear transformation T(x) = Ax is one-to-one (b) The columns of A span R3 Briefly justify your answers 1 -3 -2 2 A 2 -6 -3 7 3 -9 -6 h

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

**Find all the values of $ h $ (if any) for which**

(a) The linear transformation $ T(x) = Ax $ is one-to-one.

(b) The columns of $ A $ span $\mathbb{R}^3$.

Briefly justify your answers.

\[
A = \begin{bmatrix}
1 & -3 & -2 & 2 \\
2 & -6 & -3 & 7 \\
3 & -9 & -6 & h
\end{bmatrix}
\]

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