document.write( "Question 1161348: Let A= [-8 6 0; -9 7 0; 27 -18 1]. Find an invertible matrix X and a diagonal matrix D such that D=X^−1AX. \n" ); document.write( "
Algebra.Com's Answer #785104 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First diagonalize matrix A, that is find\r\n" );
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document.write( "D and X such that \r\n" );
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document.write( "\"A=X%2AD%2AX%5E%28-1%29\"\r\n" );
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document.write( "Left-multiply both sides by X-1\r\n" );
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document.write( "\"X%5E%28-1%29%2AA=X%5E%28-1%29%2AX%2AD%2AX%5E%28-1%29\"\r\n" );
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document.write( "Right multiply both sides by X\r\n" );
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document.write( "\"X%5E%28-1%29%2AA%2AX=X%5E%28-1%29%2AX%2AD%2AX%5E%28-1%29%2AX\"\r\n" );
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document.write( "Re=group which we can do because matrix multiplication is associative.\r\n" );
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document.write( "\"X%5E%28-1%29%2AA%2AX=%28X%5E%28-1%29%2AX%29%2AD%2A%28X%5E%28-1%29%2AX%29\"\r\n" );
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document.write( "\"X%5E%28-1%29%2AA%2AX=I%2AD%2AI%29\"\r\n" );
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document.write( "\"X%5E%28-1%29AX=D\"\r\n" );
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document.write( "\"D=X%5E%28-1%29%2AA%2AX\"\r\n" );
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document.write( "Now you diagonalize A.  If you need help let me know below\r\n" );
document.write( "and I'll get back to you by email.\r\n" );
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document.write( "Edwin
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