document.write( "Question 1185632: Use the inverse of the coefficient matrix to solve the system of equations.\r
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Algebra.Com's Answer #816469 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Write your system with all three letters and their\r\n" );
document.write( "coefficients showing (even when the coefficient is 0, 1\r\n" );
document.write( "or -1):\r\n" );
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document.write( "When we write that system as a matrix equation we have:\r\n" );
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document.write( "where A = , X = , and B =  \r\n" );
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document.write( "Now you have to calculate the inverse of matrix A, which is called\r\n" );
document.write( "the \"coefficient matrix\" because it consists of all the coefficients\r\n" );
document.write( "of the three letters:\r\n" );
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document.write( "A = \r\n" );
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document.write( "Do you know how to find the inverse of a matrix?  If not post again\r\n" );
document.write( "and we'll show you how.  I will just assume you can find that the inverse\r\n" );
document.write( "is this matrix.  I'll color it red.  It is:\r\n" );
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document.write( "      <--That's the inverse of the coefficient matrix\r\n" );
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document.write( "Next we left multiply both sides of this matrix equation:\r\n" );
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document.write( "by that red inverse matrix\r\n" );
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document.write( "and get this equation:\r\n" );
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document.write( "Now I will assume that you know how to multiply two matrices.  If\r\n" );
document.write( "you don't know how, then post again asking how to.  When you\r\n" );
document.write( "multiply the red matrices by the black matrices just to the right of\r\n" );
document.write( "each red one, you get this:\r\n" );
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document.write( "Notice that when you multiply the inverse of a matrix by the matrix\r\n" );
document.write( "of which it is the inverse you get the identity matrix, which has\r\n" );
document.write( "1's on the diagonal and 0's elsewhere.\r\n" );
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document.write( "Now if you multiply the two matrices on the left, you get:\r\n" );
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document.write( "and so x=-31, y=-126, and z=165.\r\n" );
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document.write( "Edwin

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