document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202811>Question 1202811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following augmented matrix in row-reduced form, assume that it is equivalent to an augmented matrix corresponding to a system of linear equations.\r<BR>\n" );
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document.write( "[0	1 |	−7]<BR>\n" );
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document.write( "(a.) Determine the number of equations and number of variables in the corresponding system of linear equations.\r<BR>\n" );
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document.write( "Number of Equations: 3\r<BR>\n" );
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document.write( "Number of Variables: 2\r<BR>\n" );
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document.write( "(b.) Determine whether the system is underdetermined or overdetermined.<BR>\n" );
document.write( "Underdetermined\r<BR>\n" );
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document.write( "Overdetermined    <BR>\n" );
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document.write( "(c.) Find the solution(s) to the system, if it exists. State the solution as a point, using the parameter(s) s and t if needed. If the system is inconsistent, then enter NO SOLUTION.\r<BR>\n" );
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document.write( "Part c is where I am stuck. I got all parts but part c correct, I'm not sure of an easy way or a full way of knowing how to figure this out. I got to close to the solution for x, but I'm still lost.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837967 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the following augmented matrix in row-reduced form, <BR>\n" );
document.write( "assume that it is equivalent to an augmented matrix corresponding to a system of linear equations.\r<BR>\n" );
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document.write( "[1	0 |	5]	<BR>\n" );
document.write( "[0	1 |	−7]<BR>\n" );
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document.write( "(a.) Determine the number of equations and number of variables in the corresponding system of linear equations.\r<BR>\n" );
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document.write( "Number of Equations: 3\r<BR>\n" );
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document.write( "Number of Variables: 2\r<BR>\n" );
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document.write( "(b.) Determine whether the system is underdetermined or overdetermined.<BR>\n" );
document.write( "Underdetermined\r<BR>\n" );
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document.write( "Overdetermined    <BR>\n" );
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document.write( "(c.) Find the solution(s) to the system, if it exists. State the solution as a point, using the parameter(s) s and t if needed. <BR>\n" );
document.write( "If the system is inconsistent, then enter NO SOLUTION.\r<BR>\n" );
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document.write( "Part c is where I am stuck. I got all parts but part c correct, I'm not sure of an easy way or a full way of knowing <BR>\n" );
document.write( "how to figure this out. I got to close to the solution for x, but I'm still lost. <BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This assignment is of the kind &nbsp;\" Nothing can be easier \".\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The given augmented matrix represents the system of equations\r\n" );
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document.write( "    1x + 0y =  5    (1)\r\n" );
document.write( "    0x + 1y = -7    (2)\r\n" );
document.write( "    0x + 0y =  0    (3)\r\n" );
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document.write( "It formally has two variables / unknowns x and y and three equations (1), (2) and (3).\r\n" );
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document.write( "Formally, this system is overdetermined (2 unknowns and 3 equations).\r\n" );
document.write( "But in reality, the third equation is valid for any values of x and y,\r\n" );
document.write( "so, in a meaningful context, it does not carry any information.\r\n" );
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document.write( "Therefore, we can remove it from the system and consider further TWO equations (1) and (2) only.\r\n" );
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document.write( "Then the system becomes\r\n" );
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document.write( "    x + 0y =  5    (4)\r\n" );
document.write( "    0x + y = -7    (5)\r\n" );
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document.write( "and can be written even SIMPLER\r\n" );
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document.write( "    x =  5         (6)\r\n" );
document.write( "    y = -7         (7)\r\n" );
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document.write( "These equalities, (6) and (7) represent the UNIQUE solution for the given system.\r\n" );
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document.write( "Thus the original system of three equations (1), (2) and (3) is formally overdetermined;\r\n" );
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document.write( "but in reality, it is equivalent to the CONSISTENT system of two equations (4), (5),\r\n" );
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document.write( "which has the UNIQUE solution x= 5, y= -7.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved, &nbsp;with explanations.\r<BR>\n" );
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document.write( "Hope, &nbsp;everything is clear to you.\r<BR>\n" );
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document.write( "If you still have questions, &nbsp;do not hesitate to ask.\r<BR>\n" );
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document.write( "Let's imagine for a minute, &nbsp;that the original system consists of two equations &nbsp;(1), &nbsp;(2) <BR>\n" );
document.write( "PLUS &nbsp;60 &nbsp;other equations, &nbsp;identical to equation &nbsp;(3).\r<BR>\n" );
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document.write( "Then the analysis is the same: &nbsp;this system of &nbsp;62 &nbsp;equations is overdetermined, <BR>\n" );
document.write( "but it is &nbsp;EQUIVALENT &nbsp;to the consistent system of two equations &nbsp;(1) &nbsp;and &nbsp;(2).\r<BR>\n" );
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document.write( "Again, &nbsp;it has the &nbsp;UNIQUE &nbsp;solution &nbsp;x= 5, &nbsp;y= -7.\r<BR>\n" );
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document.write( ".................\r<BR>\n" );
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document.write( "Hope, &nbsp;in the future you will not afraid such problems.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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