document.write( "Question 116768: Determine whether the matrix has an inverse. If an inverse exists, find it.
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Algebra.Com's Answer #84921 by Fombitz(32388) $\"\"$ $\"About$

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$\"A=%28matrix%282%2C2%2C-1%2C1%2C2%2C3%29%29\"$
\n" ); document.write( "A matrix has an inverse if its determinant is not equal to zero.
\n" ); document.write( "For a 2x2 matrix,
\n" ); document.write( " $\"A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\"$
\n" ); document.write( "The determinant is $\"abs%28A%29=ac-bd\"$
\n" ); document.write( "In this case the determinant is
\n" ); document.write( " $\"abs%28A%29=ac-bd=%28-1%29%283%29-%28-1%29%282%29\"$
\n" ); document.write( " $\"abs%28A%29=-3%2B2\"$
\n" ); document.write( " $\"abs%28A%29=-1\"$
\n" ); document.write( "The inverse of a 2x2 matrix is given by,
\n" ); document.write( " $\"A%5E%28-1%29=%281%2Fabs%28A%29%29%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29\"$
\n" ); document.write( "In this case
\n" ); document.write( " $\"A%5E%28-1%29=%281%2Fabs%28A%29%29%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29\"$
\n" ); document.write( " $\"A%5E%28-1%29=%281%2F-1%29%2A%28matrix%282%2C2%2C3%2C1%2C-2%2C-1%29%29\"$
\n" ); document.write( " $\"A%5E%28-1%29=%28matrix%282%2C2%2C-3%2C-1%2C2%2C1%29%29\"$ \n" ); document.write( "

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