document.write( "Question 1196243: If $\"M\"$ $\"%22%22=%22%22\"$ $\"%28matrix%283%2C3%2C1%2C-1%2Ck%2C4%2C7%2C3%2C-1%2C12%2C-2%29%29\"$
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\n" ); document.write( "Hence, if $\"X\"$ $\"%22%22=%22%22\"$ $\"%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29\"$ ,
\n" ); document.write( "Solve the equation $\"MX\"$ $\"%22%22=%22%22\"$ $\"%28matrix%283%2C1%2C1%2C11%2C21%29%29\"$
\n" ); document.write( "when k = 2, by the cofactor method. \n" ); document.write( "

Algebra.Com's Answer #831037 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "The cofactor method of finding the inverse is the hardest way.\r\n" );
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document.write( "In order to solve the equation \r\n" );
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document.write( "We must find the inverse of M which is written M^-1 by the long,\r\n" );
document.write( "hard, cofactor method:\r\n" );
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document.write( "We replace each element of M by the determinant of its cofactor, which is its\r\n" );
document.write( "minor 2x2 determinant.\r\n" );
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document.write( "We put in the \"checkerboard\" of signs, this will be the cofactor matrix\r\n" );
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document.write( "We evaluate the determinants\r\n" );
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document.write( "Next we form the adjoint or adjugate matrix which is the transpose\r\n" );
document.write( "of the matrix of cofactors:\r\n" );
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document.write( "Now we find the inverse of M by multiplying the adjoint or adjugate\r\n" );
document.write( "by the reciprocal of the value of the determinant of M. We calculated\r\n" );
document.write( "the value of the determinant of M in terms of k as\r\n" );
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document.write( "But we were told to use k=2, so substituting,\r\n" );
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document.write( "So we multiply the adjoint or adjugate by \r\n" );
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document.write( "Next we multiply both sides of the equation we are to solve:\r\n" );
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document.write( "by the inverse M^-1:\r\n" );
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document.write( "So\r\n" );
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document.write( "Edwin

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