3.3 - Math 2940 Solutions Fall 2011 Section 3 3 2(a 4 4 4 4...

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Unformatted text preview: Math 2940 Solutions, Fall 2011 Section 3 . 3 2 )(a) 4 4 4 4 4 4 4 4 4 4 4 4 → 1 1 1 1 4 4 4 4 4 4 4 4 → 1 1 1 1 0 0 0 0 0 0 0 0 . The rank is 1. 1 2 3 4 2 3 4 5 3 4 5 6 → 1 1 1 1- 1- 2- 3 3 4 5 6 → 1 1 1 1- 1- 2- 3- 2- 4- 6 → 1 1 1 1 1 2 3- 2- 4- 6 → 1 1 1 1 0 1 2 3 0 0 0 0 → 1 0- 1- 2 0 1 2 3 0 0 . The rank is 2. 1- 1 1- 1- 1 1- 1 1 1- 1 1- 1 → 1- 1 1- 1 0 0 1- 1 1- 1 → 1- 1 1- 1 0 0 0 0 . The rank is 1. 6 ) Say A has r pivotal columns. These columns form a linearly independent set whose linear combinations contains all the nonpivotal columns. The r nonzero rows of the reduced row echelon form form a linearly independent set all of whose linear combinations contain all the rows of A . Since transposing swaps rows and columns, but the number of vectors to span all the rows or columns is the same,...
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This note was uploaded on 01/02/2012 for the course MATH 2940 at Cornell.

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3.3 - Math 2940 Solutions Fall 2011 Section 3 3 2(a 4 4 4 4...

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