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9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m - 20 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.

9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m - 20 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 41EQ
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9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m - 20 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.
Transcribed Image Text:9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m - 20 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.
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for part b), how can you multiply the E1^-1 and A as they are not the same size matrix? is that possible? 

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for part (a) i don't understand how e2 can be used as the encryption key as the dimensions don't match either of the keys given as the message is a 2x4, while the keys are 2x2 and 3x3. they arent 2x4, so how could either of them be used? 

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