![\"\"](\"/images/stars/stars-12.gif\")
You can put this solution on YOUR website!
the follow cryptogram was encoded with a 2 X 2 matrix\r\n" );
document.write( "5,2,25,11,-2,-7,-15,32,14,-8,-13,38,19,-19,-19,37,16\r\n" );
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document.write( "the last word of the message is -Sue what is the message?\r\n" );
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document.write( "I am not sure what 2 by 2 matrix to use? \r\n" );
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document.write( "--------------------------------------------------------\r\n" );
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document.write( "You accidentally left out a number in the message and\r\n" );
document.write( "that caused me to have to go to a lot of trouble to \r\n" );
document.write( "discover what number you left out. But I finally\r\n" );
document.write( "found it. You left out the number -30 between the\r\n" );
document.write( "-15 and the 32. \r\n" );
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document.write( "You had this:\r\n" );
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document.write( "5,2,25,11,-2,-7,-15,32,14,-8,-13,38,19,-19,-19,37,16\r\n" );
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document.write( "and it should have been this:\r\n" );
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document.write( "5,2,25,11,-2,-7,-15,-30,32,14,-8,-13,38,19,-19,-19,37,16\r\n" );
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document.write( "Make that as this list of 1 by 2 matrices:\r\n" );
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document.write( "[5 2],[25 11],[-2 -7],[-15 -30],[32 14],[-8 -13],[38 19],[-19 -19],[37 16]\r\n" );
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document.write( "Let a blank space \"_\" be 0, let A be 1, B be 2, etc. In other\r\n" );
document.write( "words:\r\n" );
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document.write( "_=0, A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11,\r\n" );
document.write( "L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21,\r\n" );
document.write( "V=22, W=23, X=24, Y=25, Z=2600\r\n" );
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document.write( "Let the decoding matrix (the inverse of the coding matrix) be\r\n" );
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document.write( "[a b]\r\n" );
document.write( "[ ]\r\n" );
document.write( "[c d]\r\n" );
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document.write( "Don't confuse the small letters a,b,c,d with the capital letters\r\n" );
document.write( "A,B,C,D as they are different.\r\n" );
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document.write( "Since _=0, S=19, U=21, and E=5\r\n" );
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document.write( "The last two 1 by 2 matrices in the \r\n" );
document.write( "coded message \r\n" );
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document.write( "[-19 -19], [37 16]\r\n" );
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document.write( "must decode as the numbers corresponding to\r\n" );
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document.write( "[- S],[U E] \r\n" );
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document.write( "which are\r\n" );
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document.write( "[0 19],[21 5]\r\n" );
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document.write( "So [19, -19]must decode to [_ S], or [0, 19]\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( " [a b] \r\n" );
document.write( "[-19 -19]·[ ] = [0 19]\r\n" );
document.write( " [c d]\r\n" );
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document.write( "Multiplying the matrices on the left:\r\n" );
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document.write( "[-19a-19c -19b-19d] = [0 19]\r\n" );
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document.write( "So we have the equations\r\n" );
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document.write( "-19a-19c = 0\r\n" );
document.write( "-19b-19d = 19\r\n" );
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document.write( "Also 37, 16 must decode to U, E, or 21, 5\r\n" );
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document.write( " [a b] \r\n" );
document.write( "[37 16]·[ ] = [21 5]\r\n" );
document.write( " [c d]\r\n" );
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document.write( "Multiplying the matrices on the left:\r\n" );
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document.write( "[37a+16c 37b+16d] = [21 5]\r\n" );
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document.write( "So we have the equations\r\n" );
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document.write( "37a+16c = 21\r\n" );
document.write( "37b+16d = 5\r\n" );
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document.write( "So we have the four equations:\r\n" );
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document.write( "-19a-19c = 0\r\n" );
document.write( "-19b-19d = 19\r\n" );
document.write( " 37a+16c = 21\r\n" );
document.write( " 37b+16d = 5\r\n" );
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document.write( "Solving the 1st and 3rd\r\n" );
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document.write( "-19a-19c = 0\r\n" );
document.write( " 37a+16c = 21\r\n" );
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document.write( "that gives a=1 and c=-1\r\n" );
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document.write( "Solving the 2nd and 4th\r\n" );
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document.write( "-19b-19d = 19\r\n" );
document.write( " 37b+16d = 5\r\n" );
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document.write( "that gives b=1 and d=-2\r\n" );
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document.write( "So the DEcoding matrix is\r\n" );
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document.write( "[a b] [1 1]\r\n" );
document.write( "[ ] = [ ]\r\n" );
document.write( "[c d] [-1 -2]\r\n" );
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document.write( "So we start decoding\r\n" );
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document.write( "[5 2],[25 11],[-2 -7],[-15 -30],[32 14],[-8 -13],[38 19],[-19 -19],[37 16]\r\n" );
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document.write( "Decoding the [5 2]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [5 2][ ] = [5-2 5-4] = [3 1] = [C A]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [25 11]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [25 11][ ] = [25-11 25-22] = [14 3] = [N C]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [-2 -7]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [-2 -7][ ] = [-2+7 -2+14] = [5 12] = [E L]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [-15 -30]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( "[-15 -15][ ] = [-15+15 -15+30] = [0 15] = [_ O]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [32 14]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [32 14][ ] = [32-14 32-28] = [18 4] = [R D]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [-8 13]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [-8 -13][ ] = [-8+13 -8+26] = [5 18] = [E R]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "Decoding the [38 19]\r\n" );
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document.write( " [1 1]\r\n" );
document.write( " [38 19][ ] = [38-19 38-38] = [19 0] = [S _]\r\n" );
document.write( " [-1 -2]\r\n" );
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document.write( "And of course [-19 -19] decodes as [_ S] and\r\n" );
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document.write( "[37 16] decodes as [U E}\r\n" );
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document.write( "so the decoded message is\r\n" );
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document.write( "[C A},{N C],[E L],[_ O],{R D],[E R],[S _],[_ S], [U E] \r\n" );
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document.write( "CANCEL_ORDERS_ _SUE\r\n" );
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document.write( "Edwin \n" );
document.write( "