Section 1.7 Problem 3. Mark each statement True or False, and justify your answer. (T/F) The columns of a matrix A are linearly independent if the equation Ax=0 has the trivial solution. (T/F) Two vectors are linearly dependent if and only if they lie on a line through the origin. (T/F) If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S. (T/F) If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent. (T/F) The columns of any 4x5 matrix are linearly dependent. (T/F) If x and y are linearly independent, and if z is in Span (x, y), then (x, y, z) is linearly dependent. (T/F) If x and y are linearly independent, and if (x, y, z) is linearly dependent, then z is in Span (x, y). (T/F) If a set in R" is linearly dependent, then the set contains more vectors than there are entries in each vector.

Section 1.7 Problem 3. Mark each statement True or False, and justify your answer. (T/F) The columns of a matrix A are linearly independent if the equation Ax=0 has the trivial solution. (T/F) Two vectors are linearly dependent if and only if they lie on a line through the origin. (T/F) If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S. (T/F) If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent. (T/F) The columns of any 4x5 matrix are linearly dependent. (T/F) If x and y are linearly independent, and if z is in Span (x, y), then (x, y, z) is linearly dependent. (T/F) If x and y are linearly independent, and if (x, y, z) is linearly dependent, then z is in Span (x, y). (T/F) If a set in R" is linearly dependent, then the set contains more vectors than there are entries in each vector.

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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