document.write( "Question 802850: How could I know if a matrices have a unique solution, infinitely many solutions, or no solution? \n" ); document.write( "
Algebra.Com's Answer #484017 by Edwin McCravy(20077)\"\" \"About 
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document.write( "Put the matrix in row echelon form, using row operations such that:\r\n" );
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document.write( "1. All zero rows are at the bottom of the matrix. \r\n" );
document.write( "2. The element in the upper left corner is 1. \r\n" );
document.write( "3. The first nonzero element in any nonzero row is 1.\r\n" );
document.write( "4. The first nonzero element in any nonzero row can only have 0's below it.\r\n" );
document.write( "5. The leftmost nonzero element in each nonzero row after the first \r\n" );
document.write( "   occurs to the right of the leftmost nonzero element of the previous row. \r\n" );
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document.write( "To have a unique solution, the next to last element on the bottom\r\n" );
document.write( "row of the echelon form must not be 0. \r\n" );
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document.write( "To have infinitely many solutions, the last row must have all zeros. \r\n" );
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document.write( "To have no solution, the next to last element on the bottom\r\n" );
document.write( "row must be 0 and the last element on the bottom row not be zero. \r\n" );
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document.write( "Edwin
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