Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix, then the range of the transformation x→Ax is Rm. Choose the correct answer below. O A. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the columns of A. OB. The statement is false. The range of the transformation is R" because the domain of the transformation is RM OC. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the rows of A. O D. The statement is false. The range of the transformation is the set of all linear combinations of the columns of A, because each image of the transformation is of the form Ax.
Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix, then the range of the transformation x→Ax is Rm. Choose the correct answer below. O A. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the columns of A. OB. The statement is false. The range of the transformation is R" because the domain of the transformation is RM OC. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the rows of A. O D. The statement is false. The range of the transformation is the set of all linear combinations of the columns of A, because each image of the transformation is of the form Ax.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 6E
Related questions
Question
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
If A is an mxn matrix, then the range of the transformation x→Ax is Rm.
Choose the correct answer below.
O A. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the columns of
A.
OB. The statement is false. The range of the transformation is R" because the domain of the transformation is RM
OC. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the rows of A.
O D. The statement is false. The range of the transformation is the set of all linear combinations of the columns of A, because each
image of the transformation is of the form Ax.
Expert Solution
Step 1
We have to determine whether the following statement is true or false.
If A is an m×n matrix then the range of the transformation x -> Ax is R^m
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