document.write( "Question 931143: What is in verse of the coefficient matrix of the equivalent matrix equation \r
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\n" ); document.write( "x-6y=5
\n" ); document.write( " -x+4y=-5
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Algebra.Com's Answer #565466 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's one exactly like it.  Use it as a guide.\r\n" );
document.write( "Do the same things all the way through.  Just\r\n" );
document.write( "use your numbers instead:\r\n" );
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document.write( "7x - 8y = -21\r\n" );
document.write( " x -  y = -2\r\n" );
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document.write( "Write the system as:\r\n" );
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document.write( "\"7x+-+8y+=+-21\"\r\n" );
document.write( "\"1x+-+1y+=++-2\"\r\n" );
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document.write( "Then write that as:\r\n" );
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document.write( "Now we must find the inverse of the 2x2 \r\n" );
document.write( "coefficient matrix \"%28+matrix%282%2C2%2C7%2C-8%2C1%2C-1%29+%29\"\r\n" );
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document.write( "To find the inverse matrix of a 2x2 matrix:\r\n" );
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document.write( "\"%28+matrix%282%2C2%2C7%2C-8%2C1%2C-1%29+%29\"\r\n" );
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document.write( "1.  Find the value of its determinant:\r\n" );
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document.write( "\"abs%28+matrix%282%2C2%2C7%2C-8%2C1%2C-1%29%29+=+%287%29%28-1%29-%28-8%29%281%29+=+-7%2B8+=+1\"\r\n" );
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document.write( "2.  Swap the upper left and lower right elements of \"%28+matrix%282%2C2%2C7%2C-8%2C1%2C-1%29+%29\":\r\n" );
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document.write( "\"%28+matrix%282%2C2%2C-1%2C-8%2C1%2C7%29+%29\"\r\n" );
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document.write( "3. Change the sign of the upper right and lower left elements.\r\n" );
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document.write( "\"%28+matrix%282%2C2%2C-1%2C8%2C-1%2C7%29+%29\"\r\n" );
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document.write( "4. Divide every element by the value of the determinant found\r\n" );
document.write( "   in step 1.\r\n" );
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document.write( "\"%28+matrix%282%2C2%2C%28-1%29%2F1%2C8%2F1%2C%28-1%29%2F1%2C7%2F1%29+%29\"\r\n" );
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document.write( "\"%28+matrix%282%2C2%2C-1%2C8%2C-1%2C7%29+%29\"\r\n" );
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document.write( "Next we left-multiply both sides of the equation\r\n" );
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document.write( "by the inverse \"%28+matrix%282%2C2%2C-1%2C8%2C-1%2C7%29+%29\"\r\n" );
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document.write( "and we get:\r\n" );
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document.write( "Next we multiply the first two matrices on the left:\r\n" );
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document.write( "Simplifying,\r\n" );
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document.write( "Now multiply the two matrices on the left:\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "Now multiply the two matrices on the right:\r\n" );
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document.write( "Simplifying\r\n" );
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document.write( "\"+%0D%0A%28+matrix%282%2C1%2Cx%2Cy%29+%29+=+%28++matrix%282%2C1%2C21-16%2C21-14+%29%29+++\"\r\n" );
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document.write( "\"+%0D%0A%28+matrix%282%2C1%2Cx%2Cy%29+%29+=+%28++matrix%282%2C1%2C5%2C7+%29%29+++\"\r\n" );
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document.write( "So the solution is;  \"x=5\",\"y=7\"\r\n" );
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document.write( "Edwin
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