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Suppose n + m and T: R" → R™ is an onto linear transformation with standard matrix A. Check all the true statements below. A. m > n B. The column space of A is a proper subspace of R™¹ C. A has a pivot position in every row D. The null space of A is R" ✔E. The column space of A is R™ ✔F. The equation Ax = 0 has a nontrivial solution G. m

Suppose n + m and T: R" → R™ is an onto linear transformation with standard matrix A. Check all the true statements below. A. m > n B. The column space of A is a proper subspace of R™¹ C. A has a pivot position in every row D. The null space of A is R" ✔E. The column space of A is R™ ✔F. The equation Ax = 0 has a nontrivial solution G. m

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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Suppose n + m and T: R" → R™ is an onto linear transformation with standard matrix A. Check all the true statements below. A. m > n B. The column space of A is a proper subspace of R™¹ C. A has a pivot position in every row D. The null space of A is R" ✔E. The column space of A is R™ ✔F. The equation Ax = 0 has a nontrivial solution G. m <n H. A has a pivot position in every column OI. None of the above
Transcribed Image Text:Suppose n + m and T: R" → R™ is an onto linear transformation with standard matrix A. Check all the true statements below. A. m > n B. The column space of A is a proper subspace of R™¹ C. A has a pivot position in every row D. The null space of A is R" ✔E. The column space of A is R™ ✔F. The equation Ax = 0 has a nontrivial solution G. m <n H. A has a pivot position in every column OI. None of the above
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