document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=908650>Question 908650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Create coefficient matrix and augmented matrix for the following:<BR>\n" );
document.write( "Given the formula y= a(t^2) + bt + c, we can find the height, y, of an item thrown into the air. If an item is thrown and is at height, y= 23/4 at time, t= 1/2 and is at y= 7 at t= 1, and is at y= 2 at t= 2, solve for the coefficients a, b and c. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551222 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> coefficient matrix<BR>\n" );
document.write( ".25,.5,1<BR>\n" );
document.write( "4,2,1<BR>\n" );
document.write( "1,1,1<BR>\n" );
document.write( "coefficient matrix<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28%0D%0A+matrix%28+3%2C3%2C+%0D%0A.25%2C.5%2C1%2C%0D%0A4%2C2%2C1%2C%0D%0A1%2C1%2C1%0D%0A+%29%0D%0A%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "augmented decimals<BR>\n" );
document.write( ".25,.5,1|5.75<BR>\n" );
document.write( "4,2,1|2<BR>\n" );
document.write( "1,1,1|7\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28%0D%0A+matrix%28+3%2C+4%2C+%0D%0A.25%2C.5%2C1%2C5.75%2C%0D%0A4%2C2%2C1%2C2%2C%0D%0A1%2C1%2C1%2C7%0D%0A+%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "augmented fractions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28%0D%0A+matrix%28+3%2C+4%2C+%0D%0A1%2F4%2C1%2F2%2C1%2C5%263%2F4%2C%0D%0A4%2C2%2C1%2C2%2C%0D%0A1%2C1%2C1%2C7%0D%0A+%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( ".25,.5,1,5.75<BR>\n" );
document.write( "4,2,1,2<BR>\n" );
document.write( "1,1,1,7\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 1 by 0.25<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "4,2,1,2<BR>\n" );
document.write( "1,1,1,7\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-4) *row 1 to row 2<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,-6,-15,-90<BR>\n" );
document.write( "1,1,1,7\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1) *row 1 to row 3<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,-6,-15,-90<BR>\n" );
document.write( "0,-1,-3,-16\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by -6<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,1,-15/-6,15<BR>\n" );
document.write( "0,-1,-3,-16\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (1) *row 2 to row 3<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,1,5/2,15<BR>\n" );
document.write( "0,0,-1/2,-1\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by -1/2<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,1,5/2,15<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "We now have the value for the last variable.<BR>\n" );
document.write( "We will work our way up and get the other solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-5/2) *row 3 to row 2<BR>\n" );
document.write( "1,2,4,23<BR>\n" );
document.write( "0,1,0,10<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-4) *row 3 to row 1<BR>\n" );
document.write( "1,2,0,15<BR>\n" );
document.write( "0,1,0,10<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-2) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,-5<BR>\n" );
document.write( "0,1,0,10<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,-5<BR>\n" );
document.write( "0,1,0,10<BR>\n" );
document.write( "0,0,1,2<BR>\n" );
document.write( "\"-5\",\"10\",\"2\"<BR>\n" );
document.write( "(-5,10,2)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );