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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. 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
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.
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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