document.write( "Question 1179371: Consider the circuit in the figure. The currents I1, I2, and I3 in amperes are given by the solution of the system of linear equations.\r
\n" ); document.write( "\n" ); document.write( "4I1 + 8I3 = 18
\n" ); document.write( "2I2 + 8I3 = 54
\n" ); document.write( "I1 + I2 − I3 = 0
\n" ); document.write( "Use Cramer's Rule to find the three currents.
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Algebra.Com's Answer #808910 by ikleyn(52793)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Consider the circuit in the figure. The currents I1, I2, and I3 in amperes are given by the solution of the system of linear equations.
\n" ); document.write( "4I1 + 8I3 = 18
\n" ); document.write( "2I2 + 8I3 = 54
\n" ); document.write( "I1 + I2 − I3 = 0
\n" ); document.write( "Use Cramer's Rule to find the three currents.
\n" ); document.write( "I1 =
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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	4	0	8	18\r\n" );
document.write( "2	0	2	8	54\r\n" );
document.write( "3	1	1	-1	0\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	4	0	8\r\n" );
document.write( "2	0	2	8\r\n" );
document.write( "3	1	1	-1\r\n" );
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document.write( "Δ = -56\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	18	0	8\r\n" );
document.write( "2	54	2	8\r\n" );
document.write( "3	0	1	-1\r\n" );
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document.write( "Δ1 = 252\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	4	18	8\r\n" );
document.write( "2	0	54	8\r\n" );
document.write( "3	1	0	-1\r\n" );
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document.write( "Δ2 = -504\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	4	0	18\r\n" );
document.write( "2	0	2	54\r\n" );
document.write( "3	1	1	0\r\n" );
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document.write( "Δ3 = -252\r\n" );
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document.write( "x1 = Δ1 / Δ = 252 / (-56) = -9/2\r\n" );
document.write( "x2 = Δ2 / Δ = (-504) / (-56) = 9\r\n" );
document.write( "x3 = Δ3 / Δ = (-252) / (-56) = 9/2\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = -9/2\r\n" );
document.write( "x2 = 9\r\n" );
document.write( "x3 = 9/2\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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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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