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**Unformatted text preview: **E ij ) ij = 1 (the i-j entry is 1), and all other entries are 0. Show that E ij E st = E it if j = s and that E ij E st = 0 n n when j s . Show that every A R n x n is a linear combination of the various E ij . J. Show that A M n ( R ) satisfies tr ( A ) = 0 if and only if A is a linear combination of: { E ij | i j } { E jj E nn | 1 j n 1}. K. Given 1 i < j n , describe P M n ( R ) so that for any A R n x m , B = PA is the matrix A with rows i and j interchanged: row i ( B ) = row j ( A ), row j ( B ) = row i ( A ), and row k ( B ) = row k ( A ) for all k i , j . Show P has the same effect on the columns of any C R pxn . Hand In 1A) p.131. #10; 16; 26; 30; B; C; D; Fii) 1B) G; H; J; K Due Wednesday, August 31...

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