Generalize your observation. Representing a n×n identity matrix by In and a n×n

Question

Generalize your observation. Representing a n×n identity matrix by In and a n×n matrix of ones by On write an inverse for (n + 1)In On, it will be in the form of k(In + On). Enter your response by typing % before your answer. Your answer has to be in the form of INV((n + 1)In On) = k(In + On). where the k is replaced by the value you choose.

E1 = 5*eye(4)-ones ( 4, 4) E11 inv ( EI ) 2 = 6 * eye ( 5 )-ones(5,5) E2 = -1 E21 = inv (E2) E3 = 3 * eye ( 2 )-ones(2,2) 66663 11115 11111 5555 66636 1114 1112 11151 11111 5555 66366 1141 1121 11511 11111 5555 ) 63666 ) 1411 1211 15111 11111 12 5555 e 36666 4111 2111 * 51111 11111 * 21 11 11 11 11 22 22 33 EE EE EE EE EE

Explanation / Answer

Representing nxn identity matrix by ln, nxn matrix of ones by On.

Answer in the form of INV((n+1)ln-On)=k(ln+On).

By genarilizing ,we observe k is: (1/(n+1))ln

Therefore, INV((n+1)ln-On)=(1/(n+1))ln(ln+On).

For n=2==>INV(E3)=(ln/3)(ln+On)

For n=5==>INV(E3)=(ln/6)(ln+On)

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