document.write( "Question 1084062: Solve 4a-3b+c=11
\n" ); document.write( " 2a+b-4c=-1
\n" ); document.write( " a+2b-2c=1
\n" ); document.write( "By matrix inversion method \n" ); document.write( "
Algebra.Com's Answer #698119 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We convert the system of equations:\r\n" );
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document.write( "\"system%284a-3b%2Bc=11%2C%0D%0A2a%2Bb-4c=-1%2C%0D%0Aa%2B2b-2c=1%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 not post again asking how. 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, post again asking how.\r\n" );
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%2Ca%2Cb%2Cc%29%29=%28matrix%283%2C1%2C3%2C1%2C2%29%29\"\r\n" );
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document.write( "So a = 3, b= 1, c = 2.\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( "left-multiply the inverse of the coefficient matrix by \r\n" );
document.write( "the 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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