Let T: RR" be a linear transformation with standard matrix A. Which of the following is/are true? (select all that apply) If T is onto, the range of T is Rm. If T is onto, the columns of A are linearly independent. If T is onto, Ax = b has at least one solution for every b in Rm. If T is one-to-one, Ax = 0 has a nontrivial solution. If T is one-to-one, A has a pivot in every row.
Let T: RR" be a linear transformation with standard matrix A. Which of the following is/are true? (select all that apply) If T is onto, the range of T is Rm. If T is onto, the columns of A are linearly independent. If T is onto, Ax = b has at least one solution for every b in Rm. If T is one-to-one, Ax = 0 has a nontrivial solution. If T is one-to-one, A has a pivot in every row.
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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Question
![Let T: R" → R" be a linear transformation with standard matrix A. Which of the following is/are
true?
(select all that apply)
If T is onto, the range of T is Rm.
If T is onto, the columns of A are linearly independent.
If T is onto, Ax = b has at least one solution for every b in Rm.
If T is one-to-one, Ax = 0 has a nontrivial solution.
If T is one-to-one, A has a pivot in every row.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86503caa-853f-4a14-9756-7309347b5675%2F97956bc7-f8ee-441d-9617-19e52bd9fc29%2Fca1coem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T: R" → R" be a linear transformation with standard matrix A. Which of the following is/are
true?
(select all that apply)
If T is onto, the range of T is Rm.
If T is onto, the columns of A are linearly independent.
If T is onto, Ax = b has at least one solution for every b in Rm.
If T is one-to-one, Ax = 0 has a nontrivial solution.
If T is one-to-one, A has a pivot in every row.
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