document.write( "Question 1084344: Consider the following invertible matrix A, and vector B.\r
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\n" ); document.write( "\n" ); document.write( "Use Cramer's Rule to solve the following. \r
\n" ); document.write( "\n" ); document.write( "(a) Solve the equation AX = B for the variable x3 .
\n" ); document.write( "(b) Solve the equation AX = B for the variable x4 . \r
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Algebra.Com's Answer #698449 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "About Cramer's rule read 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( "    - The tricks to solve some word problems with three and more unknowns using mental math\r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of non-linear equations in three unknowns using Cramer's rule\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Now let me reveal you one secret.\r
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\n" ); document.write( "\n" ); document.write( "For matrices of dimensions 4, 5 and higher, practically nobody in nova days applies Cramer's rule with handle/manual calculations.
\n" ); document.write( "People use calculators or computer software. Very popular are internet sites that offer online solutions (solvers) for free . . . (!)\r
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\n" ); document.write( "\n" ); document.write( "One such solver you can find at the link
\n" ); document.write( "http://matrix.reshish.com/cramSolution.php\r
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\n" ); document.write( "\n" ); document.write( "http://matrix.reshish.com/cramSolution.php\r
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\n" ); document.write( "\n" ); document.write( "I used it to get the solution presented below:\r
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document.write( "Your matrix\r\n" );
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document.write( "№	X1	X2	X3	X4	X5	b\r\n" );
document.write( "1	2	4	4	3	8	3\r\n" );
document.write( "2	7	10	10	5	2	5\r\n" );
document.write( "3	1	6	8	7	5	7\r\n" );
document.write( "4	5	5	4	10	5	10\r\n" );
document.write( "5	5	1	7	6	3	6\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	X4	X5\r\n" );
document.write( "1	2	4	4	3	8\r\n" );
document.write( "2	7	10	10	5	2\r\n" );
document.write( "3	1	6	8	7	5\r\n" );
document.write( "4	5	5	4	10	5\r\n" );
document.write( "5	5	1	7	6	3\r\n" );
document.write( "D = -16605\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	X4	X5\r\n" );
document.write( "1	3	4	4	3	8\r\n" );
document.write( "2	5	10	10	5	2\r\n" );
document.write( "3	7	6	8	7	5\r\n" );
document.write( "4	10	5	4	10	5\r\n" );
document.write( "5	6	1	7	6	3\r\n" );
document.write( "D1 = 0\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	X4	X5\r\n" );
document.write( "1	2	3	4	3	8\r\n" );
document.write( "2	7	5	10	5	2\r\n" );
document.write( "3	1	7	8	7	5\r\n" );
document.write( "4	5	10	4	10	5\r\n" );
document.write( "5	5	6	7	6	3\r\n" );
document.write( "D2 = 0\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	X4	X5\r\n" );
document.write( "1	2	4	3	3	8\r\n" );
document.write( "2	7	10	5	5	2\r\n" );
document.write( "3	1	6	7	7	5\r\n" );
document.write( "4	5	5	10	10	5\r\n" );
document.write( "5	5	1	6	6	3\r\n" );
document.write( "D3 = 0\r\n" );
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document.write( "Replace the 4th column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "№	X1	X2	X3	X4	X5\r\n" );
document.write( "1	2	4	4	3	8\r\n" );
document.write( "2	7	10	10	5	2\r\n" );
document.write( "3	1	6	8	7	5\r\n" );
document.write( "4	5	5	4	10	5\r\n" );
document.write( "5	5	1	7	6	3\r\n" );
document.write( "D4 = -16605\r\n" );
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document.write( "Replace the 5th column of the main matrix with the solution vector and find its determinant\r\n" );
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document.write( "№	X1	X2	X3	X4	X5\r\n" );
document.write( "1	2	4	4	3	3\r\n" );
document.write( "2	7	10	10	5	5\r\n" );
document.write( "3	1	6	8	7	7\r\n" );
document.write( "4	5	5	4	10	10\r\n" );
document.write( "5	5	1	7	6	6\r\n" );
document.write( "D5 = 0\r\n" );
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document.write( "x1 = D1 / D = 0 / (-16605) = 0\r\n" );
document.write( "x2 = D2 / D = 0 / (-16605) = 0\r\n" );
document.write( "x3 = D3 / D = 0 / (-16605) = 0\r\n" );
document.write( "x4 = D4 / D = (-16605) / (-16605) = 1\r\n" );
document.write( "x5 = D5 / D = 0 / (-16605) = 0\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = 0\r\n" );
document.write( "x2 = 0\r\n" );
document.write( "x3 = 0\r\n" );
document.write( "x4 = 1\r\n" );
document.write( "x5 = 0\r\n" );
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