document.write( "Question 1167395: Consider the n × n matrix A where
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Algebra.Com's Answer #791996 by ikleyn(52784) $\"\"$ $\"About$

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document.write( "They are chess-board pattern matrices, filled by 1 and 0.\r\n" );
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document.write( "Regarding the rank of such a matrices, notice that they have, actually, only 2 different lines - the first and the second, \r\n" );
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document.write( "while the rest of the lines repeat either the first or the second lines.\r\n" );
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document.write( "Therefore, by using elementary linear transformations, they can be reduced to matrices having only two upper lines different,\r\n" );
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document.write( "while all other lines are zeroed.\r\n" );
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document.write( "Elementary matrix transformations do not change the range.\r\n" );
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document.write( "Therefore, the range is  2  and the null space has the dimension (n-2).\r\n" );
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document.write( "// The fact that the range is 2 means that the image of the linear operator with such a matrix has the dimension of 2.\r\n" );
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