Let T be the linear transformation whose standard matrix is given. Decide if T is a one-to-one mapping. Justify your answer. Choose the correct answer below. -7 6 9 5 2 11 -5 2 -6 - 3 - 1 10 3-15 9-25 O A. The transformation T is one-to-one because the equation T(x) = 0 has only the trivial solution. B. The transformation T is one-to-one because the equation T(x) = 0 has a nontrivial solution. O C. The transformation T is not one-to-one because the equation T(x) = 0 has a nontrivial solution. O D. The transformation T is not one-to-one because the equation T(x) = 0 has only the trivial solution.
Let T be the linear transformation whose standard matrix is given. Decide if T is a one-to-one mapping. Justify your answer. Choose the correct answer below. -7 6 9 5 2 11 -5 2 -6 - 3 - 1 10 3-15 9-25 O A. The transformation T is one-to-one because the equation T(x) = 0 has only the trivial solution. B. The transformation T is one-to-one because the equation T(x) = 0 has a nontrivial solution. O C. The transformation T is not one-to-one because the equation T(x) = 0 has a nontrivial solution. O D. The transformation T is not one-to-one because the equation T(x) = 0 has only the trivial solution.
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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![Let \( T \) be the linear transformation whose standard matrix is given. Decide if \( T \) is a one-to-one mapping. Justify your answer.
\[
\begin{bmatrix}
-7 & 6 & -6 & -1 \\
9 & 5 & 3 & 10 \\
2 & 11 & 3 & -15 \\
-5 & 2 & 9 & -25 \\
\end{bmatrix}
\]
---
Choose the correct answer below.
- \( \circ \) A. The transformation \( T \) is one-to-one because the equation \( T(x) = 0 \) has only the trivial solution.
- \( \circ \) B. The transformation \( T \) is one-to-one because the equation \( T(x) = 0 \) has a nontrivial solution.
- \( \circ \) C. The transformation \( T \) is not one-to-one because the equation \( T(x) = 0 \) has a nontrivial solution.
- \( \circ \) D. The transformation \( T \) is not one-to-one because the equation \( T(x) = 0 \) has only the trivial solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46029127-96a5-4dc2-997a-3c090d1aab2d%2Fac4c6bea-4569-4b22-bebd-e3997587ffeb%2Fjfpiizo_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( T \) be the linear transformation whose standard matrix is given. Decide if \( T \) is a one-to-one mapping. Justify your answer.
\[
\begin{bmatrix}
-7 & 6 & -6 & -1 \\
9 & 5 & 3 & 10 \\
2 & 11 & 3 & -15 \\
-5 & 2 & 9 & -25 \\
\end{bmatrix}
\]
---
Choose the correct answer below.
- \( \circ \) A. The transformation \( T \) is one-to-one because the equation \( T(x) = 0 \) has only the trivial solution.
- \( \circ \) B. The transformation \( T \) is one-to-one because the equation \( T(x) = 0 \) has a nontrivial solution.
- \( \circ \) C. The transformation \( T \) is not one-to-one because the equation \( T(x) = 0 \) has a nontrivial solution.
- \( \circ \) D. The transformation \( T \) is not one-to-one because the equation \( T(x) = 0 \) has only the trivial solution.
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