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Unformatted text preview: A is NOT equal to the column space of U . 2.4.8 If n > m then there would be more columns than rows (a fat matrix). Since the dimension of the row space is equal to the dimension of the column 1 space, there would be at least n-m free variables, and thus inFnite solu-tions. Therefore, this cannot be the case. If m > n then there would be more rows than columns (a tall matrix). If all n columns were linearly independent, then the only solution would be x = 0, and the rank would be n . Similarly, if m = n and all columns were linearly independent (and therefore rows as well) then the rank would be n as well. 2...
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- Spring '08
- Linear Algebra, column space, Dr. Jonckheere TA, Ben Raskob, U. Note