document.write( "Question 389772: Can you please help me with this problem?
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Algebra.Com's Answer #276313 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
2x-5y+7z=4
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document.write( "I will assume you already know how to find the inverse\r\n" );
document.write( "of a matrix, and how to multiply two matrices. If you don't, \r\n" );
document.write( "post again asking how.\r\n" );
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document.write( "First we form three matrices, A, X, and B.\r\n" );
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document.write( "1. Matrix A is the 3x3 coefficient matrix A, which consists \r\n" );
document.write( "of just the three columns of x, y, and z coefficients. in \r\n" );
document.write( "that order, but does not contain the column of constants.\r\n" );
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document.write( "\"A=%28matrix%283%2C3%2C2%2C-5%2C7%2C3%2C1%2C-12%2C5%2C2%2C-4%29%29\". \r\n" );
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document.write( "2. Matrix X is the 3x1 matrix of variables \"X=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29\"\r\n" );
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document.write( "3. Matrix B is the 3x1 matrix, whose only column is the\r\n" );
document.write( "column of constants: \"%28matrix%283%2C1%2C4%2C-8%2C3%29%29\"\r\n" );
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document.write( "Next we form the matrix equation:\r\n" );
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document.write( "       \"A%2AX+=+B\"\r\n" );
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document.write( "or\r\n" );
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document.write( "To solve the equation\r\n" );
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document.write( "       \"A%2AX+=+B\"\r\n" );
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document.write( "we left-multiply both sides by \"A%5E%28-1%29\", the inverse of \"A\".\r\n" );
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document.write( " \"A%5E%28-1%29%2A%28A%2AX%29+=+A%5E%28-1%29%2AB\"\r\n" );
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document.write( "Then since the associative principle holds for matrix multiplication,\r\n" );
document.write( "(even though the commutative principle DOES NOT!!!), we can move\r\n" );
document.write( "the parentheses on the left around the first two matrix factors:\r\n" );
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document.write( "\"%28A%5E%28-1%29%2AA%29%2AX+=+A%5E%28-1%29%2AB\"\r\n" );
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document.write( "Now since \"%28A%5E%28-1%29%2AA%29=I\", where I is the identity matrix, the\r\n" );
document.write( "above becomes:\r\n" );
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document.write( "\"I%2AX+=+A%5E%28-1%29%2AB\"\r\n" );
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document.write( "and by the identity property:\r\n" );
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document.write( "\"X=A%5E%28-1%29%2AB\"\r\n" );
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document.write( "Performing these operations with the actual matrices we have\r\n" );
document.write( "the equation \"AX=B\"\r\n" );
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document.write( "Next we find the inverse of A, which is written A-1.\r\n" );
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document.write( "Then we indicate the left multiplication of both sides by\r\n" );
document.write( "\"A%5E%28-1%29\" to get the equation \"A%5E%28-1%29%28A%2AX%29=A%5E%28-1%29B\":\r\n" );
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document.write( "Next we use the associative principle to move the parentheses so that\r\n" );
document.write( "they are around the first two factors to get the equation \"%28A%5E%28-1%29%2AA%29%2AX=A%5E%28-1%29%2AB\":\r\n" );
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document.write( "\"A%5E%28-1%29\" to get the equation \"A%5E%28-1%29%28A%2AX%29=A%5E%28-1%29B\":\r\n" );
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document.write( "When we perform the matrix multiplication we get:\r\n" );
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document.write( "The matrix on the left is the identity matrix\r\n" );
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document.write( "Then when we multiply the identity matrix \"I\" by the column matrix of\r\n" );
document.write( "variables, we just get the matrix of variables, or the \r\n" );
document.write( "equation \"X=A%5E%28-1%29B\"\r\n" );
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document.write( "\"%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29=%28matrix%283%2C1%2C1%2C1%2C1%29%29\"\r\n" );
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document.write( "or x=1, y=1, z=1\r\n" );
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document.write( "Edwin
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