document.write( "Question 863932: A Matrix is given. a) Determine whether the matrix is in row-echelon form. b) Determine whether the matrix is reduced row-echelon form c). write the system of equations for which the given matrix is the augmented matrix.\r
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Algebra.Com's Answer #520715 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The matrix \r\n" );
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document.write( "is in row echelon form because:\r\n" );
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document.write( "(1) every row with any non-zeros has 1 as its as its\r\n" );
document.write( "leftmost non-zero element (called its \"leading 1\".\r\n" );
document.write( "(2) the leading 1's have no non-zero elements below them,\r\n" );
document.write( "(3) the leading 1 on the 2nd row is farther to the\r\n" );
document.write( "right than the leading row in the 1st row.\r\n" );
document.write( "(4) the only all-zero row is at the bottom. \r\n" );
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document.write( "However, the matrix:\r\n" );
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document.write( "is NOT in REDUCED row-echelon form. \r\n" );
document.write( "That's because the leading (red) 1 in the \r\n" );
document.write( "second row has the non-zero (green) 2 ABOVE it.\r\n" );
document.write( "To be in REDUCED row-echelon form, the matrix\r\n" );
document.write( "must be in row echelon form, but also it must\r\n" );
document.write( "have this additional property:\r\n" );
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document.write( "The leading 1's must have no non-zero elements ABOVE them.\r\n" );
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document.write( "To get it in reduced row-echelon form\r\n" );
document.write( "we'd have to get a zero where the green 2\r\n" );
document.write( "is.  So we'd need to multiply the second row\r\n" );
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document.write( "by -2, getting\r\n" );
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document.write( "and add it element by element to the first row:\r\n" );
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document.write( "Getting:\r\n" );
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document.write( "and replace the first row by that and get:\r\n" );
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document.write( "Now it's in reduced row-echelon form, because the\r\n" );
document.write( "leading 1's have no elements above or below them,\r\n" );
document.write( "and the 2nd row's leading 1 is further to the right\r\n" );
document.write( "than the 1st row's leading 1.  Also the all-zero\r\n" );
document.write( "row is at the bottom.\r\n" );
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document.write( "----------------------------------------\r\n" );
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document.write( "The system of equations for which the  given  matrix \r\n" );
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document.write( "is the augmented matrix is this system:\r\n" );
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document.write( "Edwin

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