document.write( "Question 186735: Working with matrices and thought I had a handle on them. But this one's got me puzzled. The last row does not appear to be valid...how can zeroes = 1? Here's the problem\r
\n" ); document.write( "\n" ); document.write( "Considering the following matrix:
\n" ); document.write( "[0 1 1 0 0 | 0]
\n" ); document.write( "[0 0 0 1 0 | 0]
\n" ); document.write( "[0 0 0 0 1 | 0]
\n" ); document.write( "[0 0 0 0 0 | 1]\r
\n" ); document.write( "\n" ); document.write( "1. Is it in rref?
\n" ); document.write( "2. If it is in rref, what is the solution set?
\n" ); document.write( "3. If it is not in rref, why? \n" ); document.write( "

Algebra.Com's Answer #139983 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. Is it in rref?
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document.write( "Yes because: going left to right, the VERY FIRST non-zero element \r\n" );
document.write( "in each row which isn't all zeros has these properties:\r\n" );
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document.write( "A. It is a 1.\r\n" );
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document.write( "B. It has no elements directly above it or below it other than zeros. \r\n" );
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document.write( "C. It is farther to the right than any first non-zero element which \r\n" );
document.write( "   may be above it.\r\n" );
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document.write( "D. If any row has only zeros then it is at the bottom.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2. If it is in rref, what is the solution set?
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document.write( "There is no solution because, as you have discovered,\r\n" );
document.write( "the bottom row translates to the following equation, \r\n" );
document.write( "where the 5th variable is  \r\n" );
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document.write( "     \r\n" );
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document.write( "which has no solution, since no matter what value you\r\n" );
document.write( "substitute for  the left side will always be\r\n" );
document.write( "0 and the right side is 1, and zero can never equal 1.\r\n" );
document.write( "So the solution set is the empty set which is either\r\n" );
document.write( "written  or \r\n" );
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\n" ); document.write( "3. If it is not in rref, why?
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document.write( "But it is in rref, which means row reduced echelon form!\r\n" );
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document.write( "Edwin

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