A four-digit PIN code is required for a bank's ATM card. An encrypted code is stored with the bank account instead of storing the card's PIN code. For example, the PIN code 1234 forms the code matrix [32]. The code matrix C is then 4 multiplied by a key matrix K to obtain the encrypted matrix E. In other words, E = C · K. To determine the original PIN code from an encrypted code, the bank uses C = E · K¯¹. Suppose the key matrix is given by [1]. Determine the PIN code (in terms of a matrix) if the encrypted code is 4, 1, 4, 1.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.3: M X N Matrices
Problem 49PS
Question

Provide details/explanations of your solutions,indicate any formulas you are using and clearly show your work.

A four-digit PIN code is required for a bank's ATM card. An
encrypted code is stored with the bank account instead of
storing the card's PIN code. For example, the PIN code 1234
forms the code matrix [32]. The code matrix C is then
4
multiplied by a key matrix K to obtain the encrypted matrix E.
In other words, E = C · K. To determine the original PIN code
from an encrypted code, the bank uses C = E · K¯¹.
Suppose the key matrix is given by [1].
Determine the PIN code (in terms of a matrix) if the
encrypted code is 4, 1, 4, 1.
Transcribed Image Text:A four-digit PIN code is required for a bank's ATM card. An encrypted code is stored with the bank account instead of storing the card's PIN code. For example, the PIN code 1234 forms the code matrix [32]. The code matrix C is then 4 multiplied by a key matrix K to obtain the encrypted matrix E. In other words, E = C · K. To determine the original PIN code from an encrypted code, the bank uses C = E · K¯¹. Suppose the key matrix is given by [1]. Determine the PIN code (in terms of a matrix) if the encrypted code is 4, 1, 4, 1.
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