document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102859>Question 1102859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the inverse matrix of the following. Show your work\r<BR>\n" );
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document.write( "A=  1  1  2  1<BR>\n" );
document.write( "    1  2  2  1<BR>\n" );
document.write( "    -2 -2  -3 0<BR>\n" );
document.write( "    0   1  2  3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717632 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52818)</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=717632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Your matrix\r\n" );
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document.write( "        A1	A2	A3	A4\r\n" );
document.write( "1	1	1	2	1\r\n" );
document.write( "2	1	2	2	1\r\n" );
document.write( "3	-2	-2	-3	0\r\n" );
document.write( "4	0	1	2	3\r\n" );
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document.write( "Determinant is not zero, therefore inverse matrix exists\r\n" );
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document.write( "Write the augmented matrix\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	1	2	1	1	0	0	0\r\n" );
document.write( "2	1	2	2	1	0	1	0	0\r\n" );
document.write( "3	-2	-2	-3	0	0	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Find the pivot in the 1st column in the 1st row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	1	2	1	1	0	0	0\r\n" );
document.write( "2	1	2	2	1	0	1	0	0\r\n" );
document.write( "3	-2	-2	-3	0	0	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Subtract the 1st row from the 2nd row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	1	2	1	1	0	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	-2	-2	-3	0	0	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Multiply the 1st row by -2\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	-2	-2	-4	-2	-2	0	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	-2	-2	-3	0	0	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Subtract the 1st row from the 3rd row and restore it\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	1	2	1	1	0	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Find the pivot in the 2nd column in the 2nd row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	1	2	1	1	0	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Subtract the 2nd row from the 1st row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	2	1	2	-1	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	1	2	3	0	0	0	1\r\n" );
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document.write( "Subtract the 2nd row from the 4th row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	2	1	2	-1	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	2	3	1	-1	0	1\r\n" );
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document.write( "Find the pivot in the 3rd column in the 3rd row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	2	1	2	-1	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	2	3	1	-1	0	1\r\n" );
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document.write( "Multiply the 3rd row by 2\r\n" );
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document.write( "A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	2	1	2	-1	0	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	2	4	4	0	2	0\r\n" );
document.write( "4	0	0	2	3	1	-1	0	1\r\n" );
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document.write( "Subtract the 3rd row from the 1st row\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	-3	-2	-1	-2	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	2	4	4	0	2	0\r\n" );
document.write( "4	0	0	2	3	1	-1	0	1\r\n" );
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document.write( "Subtract the 3rd row from the 4th row and restore it\r\n" );
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document.write( "A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	-3	-2	-1	-2	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	0	-1	-3	-1	-2	1\r\n" );
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document.write( "Find the pivot in the 4th column in the 4th row (inversing the sign in the whole row)\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	-3	-2	-1	-2	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	0	1	3	1	2	-1\r\n" );
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document.write( "Multiply the 4th row by -3\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	-3	-2	-1	-2	0\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	0	-3	-9	-3	-6	3\r\n" );
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document.write( "Subtract the 4th row from the 1st row and restore it\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	0	7	2	4	-3\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	0	1	3	1	2	-1\r\n" );
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document.write( "Multiply the 4th row by 2\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	0	7	2	4	-3\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	2	2	0	1	0\r\n" );
document.write( "4	0	0	0	2	6	2	4	-2\r\n" );
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document.write( "Subtract the 4th row from the 3rd row and restore it\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	0	7	2	4	-3\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	0	-4	-2	-3	2\r\n" );
document.write( "4	0	0	0	1	3	1	2	-1\r\n" );
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document.write( "There is the inverse matrix on the right\r\n" );
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document.write( "       A1	A2	A3	A4	B1	B2	B3	B4\r\n" );
document.write( "1	1	0	0	0	7	2	4	-3\r\n" );
document.write( "2	0	1	0	0	-1	1	0	0\r\n" );
document.write( "3	0	0	1	0	-4	-2	-3	2\r\n" );
document.write( "4	0	0	0	1	3	1	2	-1\r\n" );
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document.write( "Result:\r\n" );
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document.write( "       B1	B2	B3	B4\r\n" );
document.write( "1	7	2	4	-3\r\n" );
document.write( "2	-1	1	0	0\r\n" );
document.write( "3	-4	-2	-3	2\r\n" );
document.write( "4	3	1	2	-1\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );