document.write( "Question 732098: What are the step by step instructions on finding the inverse matrices for this system of equations?:
\n" ); document.write( "2x+4y=12
\n" ); document.write( "3x-y=6 \n" ); document.write( "
Algebra.Com's Answer #447517 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here is one exactly like it.  Use it as a guide: \r\n" );
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document.write( "\"system%28x%2B2y=1%2C4x%2B5y=13%29\"\r\n" );
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document.write( "Abbreviate the above system by the AX=B form:\r\n" );
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document.write( "Now we need to find the inverse of the coefficient matrix\r\n" );
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document.write( "\"%28matrix%282%2C2%2C1%2C2%2C4%2C5%29%29\"\r\n" );
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document.write( "To find the inverse of a 2x2 matrix:\r\n" );
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document.write( "1. Interchange the upper left and lower right elements:\r\n" );
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document.write( "\"%28matrix%282%2C2%2C5%2C2%2C4%2C1%29%29\"\r\n" );
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document.write( "2. Multiply the upper right and lower left elements by -1:\r\n" );
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document.write( "\"%28matrix%282%2C2%2C5%2C-2%2C-4%2C1%29%29\"\r\n" );
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document.write( "3. Find the determinant of this matrix:\r\n" );
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document.write( "\"abs%28matrix%282%2C2%2C5%2C-2%2C-4%2C1%29%29=%285%29%281%29-%28-2%29%28-4%29=5-8=-3\"\r\n" );
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document.write( "4. Divide every element of \"%28matrix%282%2C2%2C5%2C-2%2C-4%2C1%29%29\" by this value:\r\n" );
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document.write( "5. Simplify\r\n" );
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document.write( "\"%28matrix%282%2C2%2C-5%2F3%2C2%2F3%2C4%2F3%2C-1%2F3%29%29\"\r\n" );
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document.write( "That is the inverse of the coefficient matrix.\r\n" );
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document.write( "Left-multiply both sides of the matrix\r\n" );
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document.write( "by the inverse of the coefficient matrix:\r\n" );
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document.write( "Since matrix multiplication is associative, we move\r\n" );
document.write( "the parentheses:\r\n" );
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document.write( "Now we multiply the two matrices on the far\r\n" );
document.write( "left and the far right:\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "Multiply the matrices on the left:\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"%28matrix%282%2C1%2Cx%2Cy%29%29=%28matrix%282%2C1%2C7%2C-3%29%29\" \r\n" );
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document.write( "So the solution is \r\n" );
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document.write( "\"x=7\", \"y=-3\"\r\n" );
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document.write( "Edwin

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