document.write( "Question 1141227: Greeting sir,I would like to ask a question about matrices.the question is below as shown and I need to find it by using the elimination method or the augmented matrix.I have tried to do it but it seems like I stuck because at Row 3 Column 3,(A33) I got zero as it was suppose to be 1 since it need to be identity.Can you help me to find the unknown x,y,z?\r
\n" ); document.write( "\n" ); document.write( "Solve the following systems of linear equations by using elimination method. State whether it is inconsistent or has infinitely many solutions. \r
\n" ); document.write( "\n" ); document.write( "5𝑥 −4𝑦 +𝑧 = 0
\n" ); document.write( "𝑥 +𝑦 = 0
\n" ); document.write( "−10𝑥 +8𝑦 −2𝑧 = 0
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #761756 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "A33 will only be 1 if the system of equations is consistent and has a unique solution. In this system, the 0 in A33 tells you that the system has infinitely many solutions.

\r\n" );
document.write( "   5  -4   1    0\r\n" );
document.write( "   1   1   0    0\r\n" );
document.write( " -10   8  -2    0\r\n" );
document.write( "\r\n" );
document.write( "Switch rows 1 and 2 to make A11=1; replace row 3 with row 3 plus -2 times row 1:\r\n" );
document.write( "\r\n" );
document.write( "   1   1   0    0\r\n" );
document.write( "   5  -4   1    0\r\n" );
document.write( "   0   0   0    0\r\n" );
document.write( "\r\n" );
document.write( "Replace row 2 with row 2 minus 5 times row 1, to make A21=0:\r\n" );
document.write( "\r\n" );
document.write( "   1   1   0    0\r\n" );
document.write( "   0  -9   1    0\r\n" );
document.write( "   0   0   0    0\r\n" );
document.write( "\r\n" );
document.write( "The reduced system of equations is\r\n" );
document.write( "\r\n" );
document.write( "  x+y = 0\r\n" );
document.write( "  -9y+z = 0\r\n" );
document.write( "\r\n" );
document.write( "Since both equations involve y, use y=t to define the set of solutions parametrically.\r\n" );
document.write( "\r\n" );
document.write( "  x = -y\r\n" );
document.write( "  z = 9y\r\n" );
document.write( "\r\n" );
document.write( "  y = t\r\n" );
document.write( "  x = -t\r\n" );
document.write( "  z = 9t\r\n" );
document.write( "

\n" ); document.write( "The system of equations has infinitely many solutions; the solution set is any triple (x,y,z) of the form (-t,t,9t). \n" ); document.write( "

\n" );