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
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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![**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.
\[
A = \begin{bmatrix}
1 & -3 & -2 & 2 \\
2 & -6 & -3 & 7 \\
3 & -9 & -6 & h
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f558a7-14fc-4024-84d6-4debb1adc6f6%2F1f266651-61e4-4157-b563-06eae1829a21%2F31p35t6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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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