Question

If   ` A =[a_ij]`    is a skew-symmetric matrix, then write the value of ` Σ_i  a_ij`

Answer 1

\[Given: A = \left[ a_{ij} \right] \text{is a skew - symmetric matrix }. \]

\[\]

\[ \Rightarrow a_{ij} = - a_{ij} \left[ \text{For all values of i, j} \right]\]

\[ \Rightarrow a_{ii} = - a_{ii} \left[ \text{For all values of i }\right]\]

\[ \Rightarrow a_{ij} + a_{ii} = 0\]

\[ \Rightarrow 2 a_{ii} = 0\]

\[ \Rightarrow a_{ii} = 0  \left[ \text{For all values of i} \right]\]

\[ \sum_i a_{ii} = 0 + 0 + . . . + 0 \left[\text{i times} \right]\]

\[ = 0\]

\[Thus, \]

\[ \sum_i a_{ii} = 0\]