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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.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.5: Applications Of Linear Transformations
Problem 53E
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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.
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. 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.
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