document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134169>Question 1134169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations by finding a row echelon form for the augmented matrix.<BR>\n" );
document.write( "x - 3y + 3z = 19<BR>\n" );
document.write( "2x -y - 9z= -32<BR>\n" );
document.write( "-5x+10y+z=-21\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751565 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The augmented matrix is <BR>\n" );
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document.write( "1 -3 3 19<BR>\n" );
document.write( "2 -1 -9 -32<BR>\n" );
document.write( "-5 10 1 -21<BR>\n" );
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document.write( "We perform a series of row operations to achieve row echelon form, let Rn be the nth row of the matrix<BR>\n" );
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document.write( "R3 +5R1<BR>\n" );
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document.write( "5 -15 15 95<BR>\n" );
document.write( "2 -1 -9 -32<BR>\n" );
document.write( "0 -5 16 74<BR>\n" );
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document.write( "R1/5<BR>\n" );
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document.write( "1 -3 3 19<BR>\n" );
document.write( "2 -1 -9 -32<BR>\n" );
document.write( "0 -5 16 74<BR>\n" );
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document.write( "R2 -2R1<BR>\n" );
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document.write( "2 -6 6 38<BR>\n" );
document.write( "0 5 -15 -70<BR>\n" );
document.write( "0 -5 16 74<BR>\n" );
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document.write( "R2 +R3<BR>\n" );
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document.write( "2 -6 6 19<BR>\n" );
document.write( "0 5 -15 -70<BR>\n" );
document.write( "0 0 1 4<BR>\n" );
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document.write( "R1/2, R2/5<BR>\n" );
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document.write( "1 -3 3 19<BR>\n" );
document.write( "0 1 -3 -14<BR>\n" );
document.write( "0 0 1 4<BR>\n" );
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document.write( "The above matrix is our row echelon matrix, then<BR>\n" );
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document.write( "x -3y +3z = 19<BR>\n" );
document.write( "y -3z = -14<BR>\n" );
document.write( "z = 4<BR>\n" );
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document.write( "y -3(4) = -14<BR>\n" );
document.write( "y = -2<BR>\n" );
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document.write( "x -3(-2) +3(4) = 19<BR>\n" );
document.write( "x = 1<BR>\n" );
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document.write( "x = 1, y = -2, z = 4<BR>\n" );
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document.write( "check the answers<BR>\n" );
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document.write( "x - 3y + 3z = 19<BR>\n" );
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document.write( "1 -3(-2) +3(4) = 19<BR>\n" );
document.write( "19 = 19<BR>\n" );
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document.write( "2x -y - 9z = -32<BR>\n" );
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document.write( "2(1) -(-2) -9(4) = -32<BR>\n" );
document.write( "-32 = -32<BR>\n" );
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document.write( "-5x +10y +z = -21<BR>\n" );
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document.write( "-5(1) +10(-2) +4 = -21<BR>\n" );
document.write( "-21 = -21<BR>\n" );
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document.write( "answer checks<BR>\n" );
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