document.write( "Question 1179319: Solve the system with three variables by Cramer's Rule.\r
\n" ); document.write( "\n" ); document.write( "-2x -y -3z = 3\r
\n" ); document.write( "\n" ); document.write( "2x -3y +z = -13\r
\n" ); document.write( "\n" ); document.write( "2x -3z = -11 \n" ); document.write( "
Algebra.Com's Answer #808848 by ikleyn(52806)\"\" \"About 
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\n" ); document.write( "Solve the system with three variables by Cramer's Rule.
\n" ); document.write( "-2x -y -3z = 3
\n" ); document.write( "2x -3y +z = -13
\n" ); document.write( "2x -3z = -11
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document.write( "Your matrix\r\n" );
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document.write( "        X1	X2	X3	b\r\n" );
document.write( "1	-2	-1	-3	3\r\n" );
document.write( "2	2	-3	1	-13\r\n" );
document.write( "3	2	0	-3	-11\r\n" );
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document.write( "Write down the main matrix and find its determinant\r\n" );
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document.write( "        X1	X2	X3\r\n" );
document.write( "1	-2	-1	-3\r\n" );
document.write( "2	2	-3	1\r\n" );
document.write( "3	2	0	-3\r\n" );
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document.write( "Δ = -44\r\n" );
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document.write( "Replace the 1st column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3\r\n" );
document.write( "1	3	-1	-3\r\n" );
document.write( "2	-13	-3	1\r\n" );
document.write( "3	-11	0	-3\r\n" );
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document.write( "Δ1 = 176\r\n" );
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document.write( "Replace the 2nd column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3\r\n" );
document.write( "1	-2	3	-3\r\n" );
document.write( "2	2	-13	1\r\n" );
document.write( "3	2	-11	-3\r\n" );
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document.write( "Δ2 = -88\r\n" );
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document.write( "Replace the 3rd column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "        X1	X2	X3\r\n" );
document.write( "1	-2	-1	3\r\n" );
document.write( "2	2	-3	-13\r\n" );
document.write( "3	2	0	-11\r\n" );
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document.write( "Δ3 = -44\r\n" );
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document.write( "x1 = Δ1 / Δ = 176 / (-44) = -4\r\n" );
document.write( "x2 = Δ2 / Δ = (-88) / (-44) = 2\r\n" );
document.write( "x3 = Δ3 / Δ = (-44) / (-44) = 1\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = -4\r\n" );
document.write( "x2 = 2\r\n" );
document.write( "x3 = 1\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Cramer's rule for solving systems of 3 equations in 3 unknowns see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 3x3 matrix \r
\n" ); document.write( "\n" ); document.write( "    - Co-factoring the determinant of a 3x3 matrix \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)\r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of linear equations in three unknowns using determinant (Cramer's rule)\r
\n" ); document.write( "\n" ); document.write( "    - Solving word problems by reducing to systems of linear equations in three unknowns\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "     \"3x3-Matrices, determinants, Cramer's rule for systems in three unknowns\" \r
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\n" ); document.write( "\n" ); document.write( "In addition, there are many free of charge SOLVERS on a Cramer's rule in the internet.\r
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\n" ); document.write( "\n" ); document.write( "One of such popular solvers is in this site under the link\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver\r
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