Question

E is encoding the matrix

E = (4,3)
(5,4)
Use E to decode the coded message matrix
C= (59, 13, 103, 20, 12, 7, 75, 56)
(76, 17, 130, 25 16, 9, 100,70)

Answer 1

To decode the coded message matrix C using the encoding matrix E, we need to multiply the inverse of E with C. Follow the steps provided to calculate the inverse of E and then multiply it with C.

Step-by-step explanation:

To decode the coded message matrix C using the encoding matrix E, we need to multiply the inverse of E with C. The inverse of E can be found by taking the determinant of E and then multiplying it with the adjugate of E. Let's calculate the inverse of E and then multiply it with C:

E = [4, 3] [5, 4]

Determinant of E = (4 * 4) - (3 * 5) = 16 - 15 = 1

Adjugate of E = [4, -3] [-5, 4]

Inverse of E = (1/1) * [4, -3] [-5, 4] = [4, -3] [-5, 4]

Multiplying the inverse of E with C:

[4, -3] [-5, 4] * [59, 13, 103, 20, 12, 7, 75, 56] [76, 17, 130, 25, 16, 9, 100, 70]

= [4*59 + -3*76, 4*13 + -3*17, 4*103 + -3*130, 4*20 + -3*25, 4*12 + -3*16, 4*7 + -3*9, 4*75 + -3*100, 4*56 + -3*70]

= [41, -13, 101, 5, 0, -1, 75, -28] [52, -11, 92, 10, 12, -5, 100, -28]