If possible, compute the matrix products in Exercises I through 13, using paper and pencil.
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Linear Independence Part 2 Friday, October 14, 2016 3:19 PM n Theorem:Let u ,1… , u me vectorsin R . If m > n then the set of the vectorsis linearly dependent. Proof:0 = ▯ ▯ ▯ + ▯▯ ▯▯ + ⋯+ x ▯▯ ▯▯ ▯ith an augmented matrix of [u ,1… , um, 0] has at most n pivot columns (in echelon form). Since n < m there are m + 1 columns, since n < m there must be at least one column that's not a pivot column (that is also not the last colunm). Since there is at least one solution there is a free variable and thus infinitely many solutions. Thus the set is linearly dependent. Theorem:Let u ,1… , u me a set of vectorsin R . The set is linearly dependent, if and only if one of the vectorsin in the span of the others. Proof (⇒): Assume the set is linearly
Textbook: Linear Algebra with Applications
Author: Otto Bretscher
Linear Algebra with Applications was written by and is associated to the ISBN: 9780136009269. This full solution covers the following key subjects: . This expansive textbook survival guide covers 41 chapters, and 2394 solutions. The full step-by-step solution to problem: 6 from chapter: 2.3 was answered by , our top Math solution expert on 03/15/18, 05:20PM. Since the solution to 6 from 2.3 chapter was answered, more than 242 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 4. The answer to “If possible, compute the matrix products in Exercises I through 13, using paper and pencil.” is broken down into a number of easy to follow steps, and 15 words.