document.write( "Question 772411: \r\n" );
document.write( "Evaluate the determinant |5 0 1|\r\n" );
document.write( " |4 1 2|\r\n" );
document.write( " |2 5 0|
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document.write( "
Algebra.Com's Answer #470850 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "To evaluate a 3x3 determinant, you multiply 3 numbers together\r\n" ); document.write( "6 times. as indicated by the numbers in red below, changing\r\n" ); document.write( "the signs of some, and then combine all 6 numbers:\r\n" ); document.write( "\r\n" ); document.write( "If two (or all three) of the numbers multiplied go downhill to \r\n" ); document.write( "the right like this \, you KEEP the sign. \r\n" ); document.write( "If two (or all three) of the numbers multiplied go downhill to the\r\n" ); document.write( "left like this /, you CHANGE the sign. \r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (5)(1)(0) = 0 (keep the sign) +0\r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (0)(2)(2) = 0 (keep the sign) +0\r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (1)(4)(5) = 20 (keep the sign) +20 \r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (1)(1)(2) = 2 (change the sign) -2\r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (0)(4)(0) = 0 (change the sign) -0 \r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "\r\n" ); document.write( "|5 0 1|\r\n" ); document.write( "|4 1 2| (5)(2)(5) = 50 (change the sign) -50 \r\n" ); document.write( "|2 5 0|\r\n" ); document.write( "----------------------------------------------------------------------------\r\n" ); document.write( "Now add all those 6 numbers up: 0+0+20-2-0-50 = -32\r\n" ); document.write( "\r\n" ); document.write( "Answer: -32\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |