Dadas as matrizes A=([1,-1],[2,3]) e B=([0,1],[3,8]) então, calculando-se C=(A+B)^(2) , obtém-se EXATAMENTE como resultado a matriz C . Assim sendo, assinale a alternativa CORRETA. A) C=([1,0],[60,121]) B) C=([1,0],[25,121]) C) C=([1,0],[4,8])

【Explicação】: Para resolver essa questão, devemos somar as matrizes A e B para, em seguida, calcular o quadrado da matriz resultante C.
Matrix "A" given by
1 -1
2 3

Matrix "B" =
0 1
3 8

Doing the operation of adding Matrica "A" + Matrica "B", to have matriz C
Se for C = A + B onde:

1+0 -1+1
2+3 3+8
So , investment C will be

1 0
5 11

Next we will calculate Square of C:
(C)^2 which results in :

is a 2x2 so

c[1,1] = c[1,1]*c[1,1] + c[1,2]*c[2,1] = 1*1 + 0*5 proportion C1,1= 1
c[1,2] = c[1,1]*c[1,2] + c[1,2]*c[2,2] = 1*0 + 0*11 is C1,2 =0
c[2,1] = c[2,1]*c[1,1] + c[2,2]*c[2,1] = 5* 1 + 11* 5 proportion C2,1=60
c[2,2] = c[2,1]*c[1,2] + c[2,2]*c[2,2] = 5 * 0 + 11 * 11 offer C2,2=121


Now Arranging results in matrix format we will have Caviated:
(C) ^ 2 =
1 0
60 121
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【Resposta】: A) C=(1 0 60 121)