Question

seja a matriz a3 = (aij), na qual aij = -1 se i = j 1 se i > j 0 se i < j então A - At + l3 vale?

Answer 1

$A=\left[\begin{array}{ccc}-1&0&0\\1&-1&0\\1&1&-1\end{array}\right]\\ At=\left[\begin{array}{ccc}-1&1&1\\0&-1&1\\0&0&-1\end{array}\right]\\ I3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\\\\\\ A-At=\left[\begin{array}{ccc}-1&0&0\\1&-1&0\\1&1&-1\end{array}\right]-\left[\begin{array}{ccc}-1&1&1\\0&-1&1\\0&0&-1\end{array}\right]=\left[\begin{array}{ccc}0&-1&-1\\1&0&-1\\1&1&0\end{array}\right]\\ (A-At)+I3=\left[\begin{array}{ccc}0&-1&-1\\1&0&-1\\1&1&0\end{array}\right]+\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]=\left[\begin{array}{ccc}1&-1&-1\\1&1&-1\\1&1&1\end{array}\right]$