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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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*.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 1EQ

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