document.write( "Question 661768: Use matrices to solve the system. (If the system has infinitely many solutions, express your answer in terms of c, where x = x(c), y = y(c), and z = c. If the system has no solution, enter NONE for each answer.) \r
\n" ); document.write( "\n" ); document.write( "x-2y-3z=-5
\n" ); document.write( "2x+y+z=9
\n" ); document.write( "x+3y-2z=2\r
\n" ); document.write( "\n" ); document.write( "(x,y,z)=? \n" ); document.write( "
Algebra.Com's Answer #411811 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "Hi, there--\r\n" );
document.write( "\r\n" );
document.write( "Set up your 3x4 augmented matrix using the coefficients and constants from the three \r\n" );
document.write( "equations.\r\n" );
document.write( "\r\n" );
document.write( " 1, -2, -3, -5\r\n" );
document.write( " 2, 1, 1, 9\r\n" );
document.write( " 1, 3, -2, 2\r\n" );
document.write( "\r\n" );
document.write( "(NOTE: The interface with algebra.com is not that good at drawing matrices. I typed the rows \r\n" );
document.write( "in comma-separated formate.)\r\n" );
document.write( "\r\n" );
document.write( "You want to perform a series of row operations to translate this matrix to reduced row echelon \r\n" );
document.write( "form (rref) if possible.\r\n" );
document.write( "\r\n" );
document.write( "Add -2*Row1 to Row2:\r\n" );
document.write( "1, -2, -3, -5\r\n" );
document.write( "0, 5, 7, 19\r\n" );
document.write( "1, 2, -2, 2\r\n" );
document.write( "\r\n" );
document.write( "Add -1*Row1 to Row3:\r\n" );
document.write( "\r\n" );
document.write( "1, -2, -3, -5\r\n" );
document.write( "0, 5, 7, 19\r\n" );
document.write( "0, 5, 1, 7\r\n" );
document.write( "\r\n" );
document.write( "Multiply (1/5)*Row2.\r\n" );
document.write( "\r\n" );
document.write( "1, -2, -3, -5\r\n" );
document.write( "0, 1, 7/5, 19/5\r\n" );
document.write( "0, 5, 1, 7\r\n" );
document.write( "\r\n" );
document.write( "Add 2*Row2 to Row 1\r\n" );
document.write( "\r\n" );
document.write( "1, 0, -1/5, 13/5\r\n" );
document.write( "0, 1, 7/5, 19/5\r\n" );
document.write( "0, 5, 1, 7\r\n" );
document.write( "\r\n" );
document.write( "Add -5*Row2 to Row3.\r\n" );
document.write( "\r\n" );
document.write( "1, 0, -1/5, 13/5\r\n" );
document.write( "0, 1, 7/5, 19/5\r\n" );
document.write( "0, 0, -6, -12\r\n" );
document.write( "\r\n" );
document.write( "Multiply (-1/6)*Row3.\r\n" );
document.write( "\r\n" );
document.write( "1, 0, -1/5, 13/5\r\n" );
document.write( "0, 1, 7/4, 19/5\r\n" );
document.write( "0, 0, 1, 2\r\n" );
document.write( "\r\n" );
document.write( "Add 1/5*Row3 to Row1.\r\n" );
document.write( "\r\n" );
document.write( "1, 0, 0, 3\r\n" );
document.write( "0, 1, 7/5, 19/5\r\n" );
document.write( "0, 0, 1, 2\r\n" );
document.write( "\r\n" );
document.write( "Add -7/5*Row3 to Row2.\r\n" );
document.write( "\r\n" );
document.write( "1, 0, 0, 3\r\n" );
document.write( "0, 1, 0, 1\r\n" );
document.write( "0, 0, 1, 2\r\n" );
document.write( "\r\n" );
document.write( "The matrix is now in rref. (x, y, z = 3, 1, 2)\r\n" );
document.write( "\r\n" );
document.write( "~Mrs. Figgy\r\n" );
document.write( "
\n" ); document.write( "
\n" );