document.write( "Question 1056254: Solve a system using the inverse of a 3x3 matrix.
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Algebra.Com's Answer #671419 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "6x-5y-z=31, \r\n" );
document.write( "-x+2y+z=-6, \r\n" );
document.write( "3x+3y+2z=13\r\n" );
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document.write( "We convert the system of equations:\r\n" );
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document.write( "\"system%286x-5y-z=31%2C%0D%0A-x%2B2y%2Bz=-6%2C%0D%0A3x%2B3y%2B2z=13%29\"\r\n" );
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document.write( "to the matrix equation:\r\n" );
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document.write( "I will assume that you know how to find the inverse of the \r\n" );
document.write( "coefficient matrix.  If you don't, ask me to help you in the \r\n" );
document.write( "thank-you note form below, and I'll get back to you\r\n" );
document.write( "by email. [No charge ever! I do this for fun!] \r\n" );
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document.write( "It is:\r\n" );
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document.write( "Now we left multiply both sides of the matrix equation by\r\n" );
document.write( "the inverse of the coefficient matrix:\r\n" );
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document.write( "I will also assume that you know how to multiply\r\n" );
document.write( "matrices.  If you don't, ask me to help you in the \r\n" );
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document.write( "Multiplying the matrices on the right and\r\n" );
document.write( "multiplying the first two on the left, we get:\r\n" );
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document.write( "That's the identity matrix on the left, which is what you\r\n" );
document.write( "always get when you multiply a matrix by its inverse.\r\n" );
document.write( "Multiplying the identity matrix by the column matrix of \r\n" );
document.write( "variables on the left we get\r\n" );
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document.write( "\"%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29=%28matrix%283%2C1%2C5%2C0%2C-1%29%29\"\r\n" );
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document.write( "So x = 5, y= 0, z = -1.\r\n" );
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document.write( "Even though I did the entire problem, working with the\r\n" );
document.write( "entire matrix equation, you can see that you can use a \r\n" );
document.write( "shortcut of just doing the right side only, which is to \r\n" );
document.write( "multiply the inverse of the coefficient matrix by the\r\n" );
document.write( "column matrix of constants.  That's because in every \r\n" );
document.write( "case the left side will be the same as above.  \r\n" );
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document.write( "Edwin
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