Question

1) Determine a matriz A = (aij)3x3 tal que aij = i – j.

Answer 1

 

      ( 1-1   1-2   1-3 )

A= ( 2-1   2-2   2-3 )

 

      (3-1   3-2   3-3 )

 

 

       (  0   -1    -2   )

A=  (  1     0    -1  )

 

       (  2     1     0  )

Answer 2

Bom, vamos lá. Vamos montar o esqueletodesta matriz de ordem 3.

 

$<var>A = \left(\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right) \\\\\\ \boxed{a_{ij} = i-j} \\\\ a_{11} = 1-1 = 0 \\ a_{12} = 1-2 = -1 \\ a_{13} = 1-3 = -2 \\\\ a_{21} = 2-1 = 1 \\ a_{22} = 2-2 = 0 \\ a_{23} = 2-3 = -1 \\\\ a_{31} = 3-1 = 2 \\ a_{32} = 3-2 = 1 \\ a_{33} = 3-3 = 0</var>$

 

 

Portanto, esta matriz fica:

 

$<var>A = \left(\begin{array}{ccc}0&-1&-2\\1&0&-1\\2&1&0\end{array}\right)</var>$