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Determine whether the statement below is true or false. Justify the answer. If A is a 3x2 matrix, then the transformation xAx cannot be one-to-one. Choose the correct answer below. O A. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. If Ax=b does not have a free variable, then the transformation represented by A is one-to-one. B. The statement is true. Transformations which have standard matrices which are not square cannot be one-to-one nor onto because they do not have pivot positions in every row and column. O C. The statement is true. A transformation is one-to-one only if the columns of A are linearly independent and a 3x2 matrix cannot have linearly independent columns. O D. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. It does not matter what dimensions a vector is as long as it meets this requirement. The matrix A could be 1x4 and still represent a one-to-one transformation.

Determine whether the statement below is true or false. Justify the answer. If A is a 3x2 matrix, then the transformation xAx cannot be one-to-one. Choose the correct answer below. O A. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. If Ax=b does not have a free variable, then the transformation represented by A is one-to-one. B. The statement is true. Transformations which have standard matrices which are not square cannot be one-to-one nor onto because they do not have pivot positions in every row and column. O C. The statement is true. A transformation is one-to-one only if the columns of A are linearly independent and a 3x2 matrix cannot have linearly independent columns. O D. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. It does not matter what dimensions a vector is as long as it meets this requirement. The matrix A could be 1x4 and still represent a one-to-one transformation.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 85E
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Determine whether the statement below is true or false. Justify the answer. If A is a 3x2 matrix, then the transformation X+Ax cannot be one-to-one. Choose the correct answer below. O A. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. If Ax=b does not have a free variable, then the transformation represented by A is one-to-one. B. The statement is true. Transformations which have standard matrices which are not square cannot be one-to-one nor onto because they do not have pivot positions in every row and column. O C. The statement is true. A transformation is one-to-one only if the columns of A are linearly independent and a 3x2 matrix cannot have linearly independent columns. D. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. It does not matter what dimensions a vector is as long as it meets this requirement. The matrix A could be 1x4 and still represent a one-to-one transformation.
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer. If A is a 3x2 matrix, then the transformation X+Ax cannot be one-to-one. Choose the correct answer below. O A. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. If Ax=b does not have a free variable, then the transformation represented by A is one-to-one. B. The statement is true. Transformations which have standard matrices which are not square cannot be one-to-one nor onto because they do not have pivot positions in every row and column. O C. The statement is true. A transformation is one-to-one only if the columns of A are linearly independent and a 3x2 matrix cannot have linearly independent columns. D. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. It does not matter what dimensions a vector is as long as it meets this requirement. The matrix A could be 1x4 and still represent a one-to-one transformation.
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The given statement, "If A is a 3×2 matrix, then the transformation x↦Ax cannot be one-to-one.

We have to determine whether the statement is true or false.

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