document.write( "Question 622427: You have the following matrix, and perform the following 3 row operations. What is the resultant matrix after performing these 3 row operations?\r
\n" ); document.write( "\n" ); document.write( " –R1 + R2  R2
\n" ); document.write( " 2R1 + R3  R3
\n" ); document.write( " -4R2 + R3  R3
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\n" ); document.write( " 1 0 0 10
\n" ); document.write( " 1 1 3 5
\n" ); document.write( " -2 2 0 4
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #391392 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
–R1 + R2 -> R2
\n" ); document.write( " 2R1 + R3 -> R3
\n" ); document.write( "-4R2 + R3 -> R3
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document.write( "[ 1 0 0 10] \r\n" );
document.write( "[ 1 1 3  5]\r\n" );
document.write( "[-2 2 0  4]\r\n" );
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document.write( "R1 = the first (top) row = [ 1 0 0 10] \r\n" );
document.write( "R2 = the second (middle) row = [ 1 1 3  5]\r\n" );
document.write( "R3 = the third (bottom) row = [-2 2 0  4]\r\n" );
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document.write( "First row operation:\r\n" );
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document.write( "      –R1 + R2 -> R2\r\n" );
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document.write( "Let's do the left side -R1 + R2 first.\r\n" );
document.write( "Substitute [ 1 0 0 10] for R1, [ 1 1 3  5] for R2 \r\n" );
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document.write( "–R1 + R2 = -[ 1 0 0 10] + [ 1 1 3  5] = (distribute the - sign)\r\n" );
document.write( "           [-1 0 0 -10] + [ 1 1 3  5] = (just combine corresponding elements)\r\n" );
document.write( "           [ 0 1 3  -5]                   \r\n" );
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document.write( "The \" -> R2 \" tells us to replace R2 (the 2nd row) by [ 0 1 3  -5], so\r\n" );
document.write( "the new matrix is like the old one with the middle row replaced by\r\n" );
document.write( "what we got:\r\n" );
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document.write( "[ 1 0 0 10] \r\n" );
document.write( "[ 0 1 3 -5]\r\n" );
document.write( "[-2 2 0  4]    \r\n" );
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document.write( "Now:\r\n" );
document.write( "  \r\n" );
document.write( "R1 = the first (top) row = [ 1 0 0 10] \r\n" );
document.write( "R2 = the second (middle) row = [ 0 1 3 -5]\r\n" );
document.write( "R3 = the third (bottom) row = [-2 2 0  4]\r\n" );
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document.write( "Next row operation:\r\n" );
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document.write( "     2R1 + R3 -> R3\r\n" );
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document.write( "As before, let's do the left side 2R1 + R3 first.\r\n" );
document.write( "Substitute [ 1 0 0 10] for R1, [-2 2 0  4] for R3 \r\n" );
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document.write( "2R1 + R3 = 2[ 1 0 0 10] + [-2 2 0  4] = (distribute the 2)\r\n" );
document.write( "         =  [ 2 0 0 20] + [-2 2 0  4] = (combine corresponding elements)\r\n" );
document.write( "         =  [ 0 2 0 24]\r\n" );
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document.write( "The \" -> R3 \" tells us to replace R3 (the 3rd row) by [ 0 2 0 24], so\r\n" );
document.write( "the new matrix is like the previous one with the bottom row replaced by\r\n" );
document.write( "what we got:\r\n" );
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document.write( "[ 1 0 0 10] \r\n" );
document.write( "[ 0 1 3 -5]\r\n" );
document.write( "[ 0 2 0 24]  \r\n" );
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document.write( "Edwin

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