01-sp00-ha2 - Prof. A. Suciu MTH 1101 Applications of...

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Prof. A. Suciu MTH 1101 Applications of Algebra Spring 2000 HANDOUT 2 In each of the following problems, assume the coding scheme below: A B C D E F G H I J K L M N O P 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 Q R S T U V W X Y Z blank , . ! ? 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 ( 1 ) Use the matrix M = · 21 53 ¸ to encode the message: ZAP! · ZA P ! ¸ −→ A = · 13 1 81 6 ¸ A · M = · 13 1 6 ¸ · · ¸ = · 21 10 64 40 ¸ ( 2 ) The message [ 52 , 42 , 28 , 21 , 130 , 106 , 21 , 17 , 119 , 98 , 63 , 51 , 106 , 87 , 16 , 15] was encoded using the matrix M = · 6 5 54 ¸ . (a) What is the matrix form of the message? A · M = 52 42 28 21 130 106 21 17 119 98 63 51 106 87 16 15 (b) What matrix is needed for decoding the message? M 1 = 1 6 · 4 ( 5) · ( 5) · · 4 ( 5) ( 5) 6 ¸ =( 1) · · 45 56 ¸ = · 4 5 5 6 ¸ (c) What is the message?
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