Question

construa a matriz A = (aij) 2x2, tal que:

aij = 1, se i = j
aij = 0, se i diferente j

Answer 1

$2 X 2 : \left[\begin{array}{ccc} a_{11} & a_{12} \\ a_{21} & a_{22} \\\end{array}\right]$


$i = j \to { a_{11} , a_{22} } ( 1 )\\ i \neq j \to a_{12} , a_{21} (0)$

$matriz : \\ \\ \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]$

Answer 2

$\begin{vmatrix} x_{11} & x_{12} \\ x_{21} & x_{22} \end{vmatrix} \\\\ \texttt{Quando i = j}\\\\ x_{11} = 1\\\\ x_{22} = 1\\\\ \begin{vmatrix} x_{1} & x_{12} \\ x_{21} & x_{1} \end{vmatrix}\\\\ \texttt{Quando i e diferente de j}\\\\ x_{12} = 0\\\\ x_{21} = 0\\\\ \boxed{\begin{bmatrix} 1 & 0\\ 0&1 \end{bmatrix}}\\\\ \texttt{Podemos observar que se trata de uma matriz identidade.}$