Question

determine a soma dos elementos da diagonal principal com os elementos da diagonal secundária da matriz A=(aij) de ordem 4, em que aij= i- j

Answer 1

$A=\left[\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a{34}\\a_{41}&a_{42}&a_{43}&a_{44}\end{array}\right] \\ \\ A=\left[\begin{array}{cccc}1-1&1-2&1-3&1-4}\\2-1&2-2&2-3&2-4\\3-1}&3-2&3-3&3-4\\4-1&4-2&4-3&4-4\end{array}\right] \\ \\ A=\left[\begin{array}{cccc}0&-1&-2&-3}\\1&0&-1&-2\\2}&1&0&-1\\3&2&1&0\end{array}\right] \\ \\ \boxed{\boxed{0+0+0+0+3+1+(-1)+(-3)=0}}$