document.write( "Question 66250This question is from textbook
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Solve the linear system using the given\r\n" );
document.write( " inverse of the coefficent matrix. \r\n" );
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document.write( " w + 6x + 3y - 3z = 2\r\n" );
document.write( "2w + 7x +  y + 2z = 5\r\n" );
document.write( " w + 5x + 3y - 3z = 3\r\n" );
document.write( "   - 6x - 2y + 3z = 6\r\n" );
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document.write( "A-1 = \r\n" );
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document.write( "Do I plug in the number from the inverse coefficent matrix\r\n" );
document.write( "into the linear system, and then possibly use Cramer's Rule?

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Algebra.Com's Answer #47004 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Solve the linear system using the given\r\n" );
document.write( " inverse of the coefficent matrix. \r\n" );
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document.write( " w + 6x + 3y - 3z = 2\r\n" );
document.write( "2w + 7x +  y + 2z = 5\r\n" );
document.write( " w + 5x + 3y - 3z = 3\r\n" );
document.write( "   - 6x - 2y + 3z = 6\r\n" );
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document.write( "A-1 = \r\n" );
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document.write( "Do I plug in the number from the inverse coefficent matrix\r\n" );
document.write( "into the linear system, and then possibly use Cramer's Rule?\r\n" );
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document.write( "No, no. This has nothing whatsoever to do with Cramer's rule.\r\n" );
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document.write( "If not, how do I even begin this problem??\r\n" );
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document.write( "First of all you have to know how to multiply two matrices\r\n" );
document.write( "before you can do this problem.  If you don't know how,\r\n" );
document.write( "then post again asking how to do it.  Or maybe your teacher\r\n" );
document.write( "will let you do it on the calculator.\r\n" );
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document.write( "A =  = the coefficient matrix\r\n" );
document.write( "X = \"%28matrix%284%2C1%2Cw%2Cx%2Cy%2Cz%29%29\" = the column vector of unknowns\r\n" );
document.write( "B = \"%28matrix%284%2C1%2C2%2C5%2C3%2C6%29%29\" = the column vector of constants\r\n" );
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document.write( "The steps are:\r\n" );
document.write( "                              AX = B\r\n" );
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document.write( "Left-multiply both sides by the inverse matrix of matrix A,\r\n" );
document.write( "which is denoted by A-1:\r\n" );
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document.write( "                           A-1AX = A-1B\r\n" );
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document.write( "When you multiply a matrix by its inverse you get the identity matrix I\r\n" );
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document.write( "                              IX = A-1B\r\n" );
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document.write( "When you multiply the identity matrix I by a matrix X you just get X\r\n" );
document.write( "(It's just like multiplying x by 1 and getting x in ordinary algebra)\r\n" );
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document.write( "                               X = A-1B\r\n" );
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document.write( "You start with the matrix equation   \r\n" );
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document.write( "                              AX = B\r\n" );
document.write( "which is        \r\n" );
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document.write( "                 \"%28matrix%284%2C1%2Cw%2Cx%2Cy%2Cz%29%29\" = \"%28matrix%284%2C1%2C2%2C5%2C3%2C6%29%29\"\r\n" );
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document.write( "Then you left-multiply both sides by the inverse matrix:\r\n" );
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document.write( "                           A-1AX = A-1B\r\n" );
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document.write( "which is\r\n" );
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document.write( "   \"%28matrix%284%2C1%2Cw%2Cx%2Cy%2Cz%29%29\" =  \"%28matrix%284%2C1%2C2%2C5%2C3%2C6%29%29\"\r\n" );
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document.write( "Then you PERFORM the multiplication of the two 4×4 matrices A and \r\n" );
document.write( "A-1 on the left, which will give I, the identity matrix.  Also \r\n" );
document.write( "PERFORM the multiplication of the 4×4 matrix A-1 by the 4×1 matrix\r\n" );
document.write( "B on the right:\r\n" );
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document.write( "                              IX = A-1B\r\n" );
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document.write( "                    \"%28matrix%28+4%2C+4%2C+1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%29%29\"\"%28matrix%284%2C1%2Cw%2Cx%2Cy%2Cz%29%29\" = \"%28matrix%284%2C1%2C20%2C-1%2C-12%2C-8%29%29\"\r\n" );
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document.write( "It always turns out that when you multiply a matrix by its inverse,\r\n" );
document.write( "you get the identity matrix, I, which has 1's down the main diagonal \r\n" );
document.write( "and zeros elsewhere.  Now when you multiply that identity matrix\r\n" );
document.write( "by the 4×1 matrix which has only the four letters w,x,y,z, in it\r\n" );
document.write( "you just get that same 4×1 matrix, so you have:\r\n" );
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document.write( "                               X = A-1B\r\n" );
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document.write( "                            \"%28matrix%284%2C1%2Cw%2Cx%2Cy%2Cz%29%29\" = \"%28matrix%284%2C1%2C20%2C-1%2C-12%2C-8%29%29\"\r\n" );
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document.write( "That means of course that w = 20, x = -1, y = -12, z = -8  \r\n" );
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document.write( "Edwin
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