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Unformatted text preview: 1 2 54 1 4 2141 . Determine whether or not T is onetoone and whether or not T is onto. Explain. This matrix can be row reduced to 1 2 54 0 1 4 2 0 0 0 1 . As there is a pivot in every row, we know that if A represents the above matrix, then A x = b has a solution for all b R 3 so it follows that T is onto. T is not onetoone; however. One way to see this is that as A contains more column vectors then rows, the column vectors have to be linearly dependent. Another way to see this is that if we solve A x = 0 then from the above row reduction, the variable x 3 must be free so we can have nontrivial solutions to A x = 0 . 2...
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at University of California, Berkeley.
 Fall '10
 yildiz
 Math

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