Calcule o traço da matriz A abaixo.
A=[cccccccccccccccccccccc 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.529 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.848 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.929 & 0 & 0 & 0 & 0 & 0 & 0 & 1 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.372 & 0 & 0 & 0 & 0 & 0 & 0 & 0 -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.640 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -0.768 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.781 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.372 & 0 & 0 & 0 & 0 & 0 0 & 0 0 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.929 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -0.372 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.929 & 0.929 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.372 & 0.372 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.529 & 0 & 0 & 0 & -0.929 & 0.929 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0.484 & 0 & 0 & 0 & -0.372 & 0.372 & 0 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.640 & 0 & 0 & 0 & -0.929 & 0.929 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0.768 & 0 & 0 & 0 & -0.372 & 0.372 & 0 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.781 & 0 & 0 & 0 & -0.929 & 0.929 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0.625 & 0 & 0 & 0 & -0.372 & 0.372 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -0.929 & 0 & 0 & -0.929 & 0.929 & 0 & 0 & 0 & 0 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0.372 & 0 & 0 & -0.372 & 0.372 & 0 & 0 & 0 & 0 ]

Passo 1

O enunciado pede para calcular o traço da matriz A, isto é, a soma dos elementos da diagonal principal. Este conteúdo pertence ao tópico de operações com matrizes, especificamente ao conceito de traço.

Passo 2

O traço de uma matriz A de ordem n é definido por tr(A)=sumi=1^nAii. Então basta identificar cada elemento diagonal Aii e somá-los.

Passo 3

Analisando cada linha i e pegando o elemento na coluna i, vemos que todos os Aii são zero, exceto:
  • A11=1
  • A8,8=-1
  • A16,16=0.929
    Os demais diagonais são nulos.

Passo 4

Somando esses valores temos:
tr(A)=1 + (-1) + 0.929 = 0.929.

Resposta

0.929

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