document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2887>Question 2887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help on these three problems....................<BR>\n" );
document.write( "(1).<BR>\n" );
document.write( "-4     5 <BR>\n" );
document.write( "-5<BR>\n" );
document.write( "The determinant of the matrix A is 1. Find the missing element of the matrix A<BR>\n" );
document.write( "a.1<BR>\n" );
document.write( "b.3<BR>\n" );
document.write( "c.6<BR>\n" );
document.write( "d.–24<BR>\n" );
document.write( "(2). Find the determinant of the matrix C.<BR>\n" );
document.write( "C=<BR>\n" );
document.write( "4  0  –7 <BR>\n" );
document.write( "3  0  6<BR>\n" );
document.write( "-5  2  3<BR>\n" );
document.write( "  <BR>\n" );
document.write( "a.45<BR>\n" );
document.write( "b.24<BR>\n" );
document.write( "c.-90<BR>\n" );
document.write( "d.-21\r<BR>\n" );
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document.write( "(3). Use Cramer’s Rule to solve y.<BR>\n" );
document.write( "x-4y=4<BR>\n" );
document.write( "4x-y=1\r<BR>\n" );
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document.write( "a.-8/15<BR>\n" );
document.write( "b. –1<BR>\n" );
document.write( "c. 17/5<BR>\n" );
document.write( "d. 0<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1257 by </B><A HREF=/tutors/aboutme.mpl?userid=xcentaur><B>xcentaur(357)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=xcentaur><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [1]<BR>\n" );
document.write( "-4     5 <BR>\n" );
document.write( "-5     X<BR>\n" );
document.write( "\"The determinant of the matrix A is 1.\"<BR>\n" );
document.write( "<br><I><BR>\n" );
document.write( "In matrix X=<TABLE  border=1>\n" );
document.write( "<tr><td>a<td>b<tr><td>c<td>d\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Determinant = ab - cd<BR>\n" );
document.write( "</i><br><BR>\n" );
document.write( "Determinant = (-4*X)-(-5*5)<BR>\n" );
document.write( "            = -4X+25<BR>\n" );
document.write( "Since we know the determinant is one,<BR>\n" );
document.write( "1=-4X+25<BR>\n" );
document.write( "-4X=-24<BR>\n" );
document.write( "X=-24/-4<BR>\n" );
document.write( " =6<BR>\n" );
document.write( "Therefore,correct answer is: <B>c.6</b><BR>\n" );
document.write( "<P><BR>\n" );
document.write( "[2]<BR>\n" );
document.write( "Matrix C=<BR>\n" );
document.write( "<TABLE  border=1>\n" );
document.write( "\r\n" );
document.write( "<tr><td>+4<td>0<td>–7 \r\n" );
document.write( "<tr><td>+3<td>0<td>+6\r\n" );
document.write( "<tr><td>-5<td>+2<td>+3\r\n" );
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document.write( "</TABLE><BR>\n" );
document.write( "In matrix X of order 3=<BR>\n" );
document.write( "<TABLE  border=1>\n" );
document.write( "\r\n" );
document.write( "<tr><td>x1<td>x2<td>x3 \r\n" );
document.write( "<tr><td>y1<td>y2<td>y3\r\n" );
document.write( "<tr><td>z1<td>z2<td>z3\r\n" );
document.write( "\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Determinant of X is=<BR>\n" );
document.write( "=x1(y2z3-y3z2)-x2(y1z3-y3z1)+x3(y1z2-z1y2)<BR>\n" );
document.write( "Determinant of C is=<BR>\n" );
document.write( "= 4[0*3-(2*6)]-0[3*3-(-5*6)]+(-7)[3*2-(-5*0)]<BR>\n" );
document.write( "= 4[0-12]-0[9+30]-7[6-0]<BR>\n" );
document.write( "= 4[-12]-0[39]-7[6]<BR>\n" );
document.write( "= -48-0-42<BR>\n" );
document.write( "= -90<BR>\n" );
document.write( "<br>Therefore,correct answer is: <B>c.-90</b><BR>\n" );
document.write( "<P><BR>\n" );
document.write( "[3]<BR>\n" );
document.write( "Cramer's Rule - Given the system<BR>\n" );
document.write( "p1x + q1y = c1 ... [eqn1]<BR>\n" );
document.write( "p2x + q2y = c2 ... [eqn2]\r<BR>\n" );
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document.write( "Determinant detA = p1q2 - p2q1<BR>\n" );
document.write( "Determinant detX = c1q2 - c2q1<BR>\n" );
document.write( "Determinant detY = p1c2 - p2c1\r<BR>\n" );
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document.write( "Then x=detX/detA<BR>\n" );
document.write( "Then y=detY/detA<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Cramer’s Rule to solve y.<BR>\n" );
document.write( "x-4y=4<BR>\n" );
document.write( "4x-y=1<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Consider the determinant formed by the x,y and constant term of the given equations.<BR>\n" );
document.write( "<TABLE  border=1>\n" );
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document.write( "<tr><td><b>p</b><td><b>q</b><td><b>c</b>\r\n" );
document.write( "<tr><td>+1<td>-4<td>4\r\n" );
document.write( "<tr><td>+4<td>-1<td>1\r\n" );
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document.write( "</TABLE><br>\r<BR>\n" );
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document.write( "detA = p1q2 - p2q1<BR>\n" );
document.write( "=(1*-1)-(4*-4)<BR>\n" );
document.write( "=-1-(-16)<BR>\n" );
document.write( "=-1+16<BR>\n" );
document.write( "=15<BR>\n" );
document.write( "detY = p1c2 - p2c1<BR>\n" );
document.write( "=(1*1)-(4*4)<BR>\n" );
document.write( "=1-16<BR>\n" );
document.write( "=-15<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "By Cramer's Rule,y=detY/detA<BR>\n" );
document.write( "y=-15/15<BR>\n" );
document.write( "=-1<BR>\n" );
document.write( "<br>Therefore,the correct answer is: <B>b. –1</b><BR>\n" );
document.write( "<P><BR>\n" );
document.write( "Hope this helps,<BR>\n" );
document.write( "best of luck.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );