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The linear transformation T: R$ →→R with standard matrix A is onto. There may be more than one correct answer. ✔A. The columns of A are linearly dependent. ✔B. The columns of A span Rt. C. Each b in R* is a linear combination of the columns of A. ✓D. There exists a b in IR* such that the equation 7(x) = b has a solution. ✓E. The equation T(x) = b has a solution for all b in R*.

The linear transformation T: R$ →→R with standard matrix A is onto. There may be more than one correct answer. ✔A. The columns of A are linearly dependent. ✔B. The columns of A span Rt. C. Each b in R* is a linear combination of the columns of A. ✓D. There exists a b in IR* such that the equation 7(x) = b has a solution. ✓E. The equation T(x) = b has a solution for all b in R*.

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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The linear transformation T: R$ →→R with standard matrix A is onto. There may be more than one correct answer. A. The columns of A are linearly dependent. B. The columns of A span R¹. C. Each b in R* is a linear combination of the columns of A. ✓D. There exists a b in R* such that the equation T(x) = b has a solution. ✓E. The equation T(x) = b has a solution for all b in IR*. OF. The HLS Ax = 0 has a nontrivial solution. G. The matrix A has a pivot in every column. ✓H. The equation T(x) = 0 has a nontrivial solution. ✓1. The matrix A has a pivot in every row. J. None of the above
Transcribed Image Text:The linear transformation T: R$ →→R with standard matrix A is onto. There may be more than one correct answer. A. The columns of A are linearly dependent. B. The columns of A span R¹. C. Each b in R* is a linear combination of the columns of A. ✓D. There exists a b in R* such that the equation T(x) = b has a solution. ✓E. The equation T(x) = b has a solution for all b in IR*. OF. The HLS Ax = 0 has a nontrivial solution. G. The matrix A has a pivot in every column. ✓H. The equation T(x) = 0 has a nontrivial solution. ✓1. The matrix A has a pivot in every row. J. None of the above
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