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Φ0[ n] = 1 for all integer n φ1[ n] = e jπn. Therefore, we conclude dim Col( A) + dim Nul( AT ) = m.

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Also, rank AT = rank A = dim Col( A). Homework 7: Solutions 1.

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Energy distribution N( ) d = C. A grade of 0 indicates no solution or a substantially wrong solution. C is routed from one building in which it is generated to an adjoining building in which it is used for space heating. By the Rank Theorem, rank AT + dim Nul( AT ) = m.

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