document.write( "Question 1055150: Inverse matrix of 2X+3y=5
\n" ); document.write( "4X-2y=7 \n" ); document.write( "

Algebra.Com's Answer #670344 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Inverse matrix of the coefficient matrix is what I think you're asking for.
\n" ); document.write( " $\"A=%28matrix%282%2C2%2C%0D%0A2%2C3%2C%0D%0A4%2C-2%29%29\"$
\n" ); document.write( "For a 2x2 system,
\n" ); document.write( " $\"B=%28matrix%282%2C2%2C%0D%0Aa%2Cb%2Cc%2Cd%29%29\"$
\n" ); document.write( "the inverse matrix is,
\n" ); document.write( " $\"B%5E%28-1%29=%281%2FD%29%2A%28matrix%282%2C2%2C%0D%0Ad%2C-b%2C-c%2Ca%29%29\"$
\n" ); document.write( "where the determinant, $\"D=1%2F%28ad-bc%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"D=1%2F%282%28-2%29-4%28-3%29%29%29=1%2F%28-4-12%29=-1%2F16\"$
\n" ); document.write( "and
\n" ); document.write( " $\"A%5E%28-1%29=%28-1%2F16%29%2A%28matrix%282%2C2%2C-2%2C-3%2C-4%2C2%29%29\"$
\n" ); document.write( " $\"A%5E%28-1%29=%28matrix%282%2C2%2C%0D%0A1%2F8%2C3%2F16%2C1%2F4%2C-1%2F8%29%29\"$ \r
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