Dadas as matrizes
\underset{\sim}{A}=\left[\begin{array}{cc}2 & -1 \\\\ 0 & 5 \\\\ 3 & 4\end{array}\right] e \underset{\sim}{B}=\left[\begin{array}{cc}1 & 3 \\\\ 2 & -4 \\\\ -2 & 6\end{array}\right], calcule:
\underset{\sim}{A}-\underset{\sim}{B}

Passo 1

O enunciado nos dá as matrizes \underset{\sim}{A}=\left[\begin{array}{cc}2 & -1 \\[4pt]0 & 5 \\[4pt]3 & 4\end{array}\right] e \underset{\sim}{B}=\left[\begin{array}{cc}1 & 3 \\[4pt]2 & -4 \\[4pt]-2 & 6\end{array}\right]
ambas de dimensão 3\times2, e pede o cálculo de \underset{\sim}{A}-\underset{\sim}{B}.
O conteúdo aqui é subtração de matrizes, que se faz elemento a elemento.]

Passo 2

Pela definição,
(\underset{\sim}{A}-\underset{\sim}{B})_{ij} \;=\; A_{ij} - B_{ij}.
Logo, aplicando isto linha a linha, temos
\underset{\sim}{A}-\underset{\sim}{B} =\left[\begin{array}{cc} 2-1 & -1-3 \\[4pt] 0-2 & 5-(-4) \\[4pt] 3-(-2) & 4-6 \end{array}\right] =\left[\begin{array}{cc} 1 & -4 \\[4pt] -2 & 9 \\[4pt] 5 & -2 \end{array}\right].]

Resposta

\underset{\sim}{A}-\underset{\sim}{B} =\left[\begin{array}{cc} 1 & -4 \\[4pt] -2 & 9 \\[4pt] 5 & -2 \end{array}\right].]

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