Let T : R" → R" be a linear transformation with standard matrix A. Which of the following is not a characterization of the statement “T is surjective"? O A. RREF(A) has a pivot in every row О в. Im T = R" Oc. The columns of A span R" O D. RREF(A) has a pivot in every column

Let T : R" → R" be a linear transformation with standard matrix A. Which of the following is not a characterization of the statement “T is surjective"? O A. RREF(A) has a pivot in every row О в. Im T = R" Oc. The columns of A span R" O D. RREF(A) has a pivot in every column

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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A: See the detailed solution below.

Question

Let T : R" → R" be a linear transformation with standard matrix A. Which of the following is not a
characterization of the statement “T is surjective"?
OA.
RREF(A) has a pivot in every row
О в.
Im T = R"
Oc.
The columns of A span R"
OD.
RREF(A) has a pivot in every column

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