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Unformatted text preview: 1 2 5-4 1 4 2-1-4-1 . Determine whether or not T is one-to-one and whether or not T is onto. Explain. This matrix can be row reduced to 1 2 5-4 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 one-to-one; 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