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Which of the following statements is true? OA is a 4x 3 matrix, then the transformation x→ Ax cannot be one to one. O When two linear transformations are performed one after another, the combined effect may not always be a linear transformation. Amapping T: R-R" is one to one if each vector in R" maps onto a unique vector in R O The columns of the standard matrix for a linear transformation T:R"R" are the images of the columns of the n x n identity matrix O Not every linear transformation T: R-R" is a matrix transformation

Which of the following statements is true? OA is a 4x 3 matrix, then the transformation x→ Ax cannot be one to one. O When two linear transformations are performed one after another, the combined effect may not always be a linear transformation. Amapping T: R-R" is one to one if each vector in R" maps onto a unique vector in R O The columns of the standard matrix for a linear transformation T:R"R" are the images of the columns of the n x n identity matrix O Not every linear transformation T: R-R" is a matrix transformation

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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Which of the following statements is true? OA is a 4 x 3 matrix, then the transformation x→ Ax cannot be one to one. O When two linear transformations are performed one after another, the combined effect may not always be a linear transformation. O Amapping T: RR is one to one if each vector in R" maps onto a unique vector in R™ O The columns of the standard matrix for a linear transformation T: R"R" are the images of the columns of the n x n identity matrix O Not every linear transformation T: R"R" is a matrix transformation
Transcribed Image Text:Which of the following statements is true? OA is a 4 x 3 matrix, then the transformation x→ Ax cannot be one to one. O When two linear transformations are performed one after another, the combined effect may not always be a linear transformation. O Amapping T: RR is one to one if each vector in R" maps onto a unique vector in R™ O The columns of the standard matrix for a linear transformation T: R"R" are the images of the columns of the n x n identity matrix O Not every linear transformation T: R"R" is a matrix transformation
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