document.write( "Question 824578: solve the following linear equations using matrix techniques:
\n" ); document.write( "3x1+5x2=1
\n" ); document.write( "x1+2x2=2 \n" ); document.write( "
Algebra.Com's Answer #496603 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Since algebra.com doesn't do matrices very well, I will just be showing the rectangular array of numbers.

\n" ); document.write( "\"3x%5B1%5D%2B5x%5B2%5D=1\"
\n" ); document.write( "\"x%5B1%5D%2B2x%5B2%5D=2\"
\n" ); document.write( "translates into the augmented matrix:
\n" ); document.write( "
\r\n" );
document.write( "   3   5   1\r\n" );
document.write( "   1   2   2\r\n" );
document.write( "Since a 1 in row 1 column 1 is desired, I'll swap the rows:\r\n" );
document.write( "   1   2   2\r\n" );
document.write( "   3   5   1\r\n" );
document.write( "Adding -3 times row 1 to row 2:\r\n" );
document.write( "   1   2   2\r\n" );
document.write( "   0  -1  -5\r\n" );
document.write( "Adding 2 times row 2 to row 1:\r\n" );
document.write( "   1   0  -8\r\n" );
document.write( "   0  -1  -5\r\n" );
document.write( "Multiplying row 2 by -1:\r\n" );
document.write( "   1   0  -8\r\n" );
document.write( "   0   1   5\r\n" );
document.write( "
which translates back into:
\n" ); document.write( "\"x%5B1%5D+=+-8\"
\n" ); document.write( "\"x%5B2%5D+=+5\" \n" ); document.write( "
\n" );