document.write( "Question 1179993: Use determinate method to solve
\n" ); document.write( "2x+3y-4z=-4
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Algebra.Com's Answer #809569 by ikleyn(52790)\"\" \"About 
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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	3	-4	-4\r\n" );
document.write( "2	1	-2	2	3\r\n" );
document.write( "3	1	3	-2	1\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	3	-4\r\n" );
document.write( "2	1	-2	2\r\n" );
document.write( "3	1	3	-2\r\n" );
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document.write( "Δ = -12\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	-4	3	-4\r\n" );
document.write( "2	3	-2	2\r\n" );
document.write( "3	1	3	-2\r\n" );
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document.write( "Δ1 = -12\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	-4	-4\r\n" );
document.write( "2	1	3	2\r\n" );
document.write( "3	1	1	-2\r\n" );
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document.write( "Δ2 = -24\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	3	-4\r\n" );
document.write( "2	1	-2	3\r\n" );
document.write( "3	1	3	1\r\n" );
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document.write( "Δ3 = -36\r\n" );
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document.write( "x1 = Δ1 / Δ = (-12) / (-12) = 1\r\n" );
document.write( "x2 = Δ2 / Δ = (-24) / (-12) = 2\r\n" );
document.write( "x3 = Δ3 / Δ = (-36) / (-12) = 3\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 1\r\n" );
document.write( "x2 = 2\r\n" );
document.write( "x3 = 3\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
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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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