Question

Determine as seguintes matrizes:
a) B = (bij)3x3 tal que bij = (i-j)²
b) C= (cij)2x3 tal que cij= {2,se i=j i+j,se i≠j}

Answer 1

a) 

$B = \left[\begin{array}{ccc} b_{11} &b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right] \\ \\ \\ b_{ij}= (i-j)^{2} \\b_{11} = (1-1)^{2} =0^{2}=0 \\b_{12} = (1-2)^{2}=(-1)^{2}=1 \\b_{13} = (1-3)^{2}=(-2)^{2}=4 \\b_{21} = (2-1)^{2}=1^{2}=1 \\b_{22} = (2-2)^{2}=0^{2}=0 \\b_{23}=(2-3)^{2} = (-1)^{2}=1 \\b_{31}=(3-1)^{2}=2^{2}=4 \\b_{32} =(3-2)^{2}=1^{2}=1 \\b_{33} = (3-3)^{2} =0^{2}=0$

$B = \left[\begin{array}{ccc} 0 &1&4\\1&0&1\\4&1&0\end{array}\right]$

b)

$C = \left[\begin{array}{ccc} c_{11} &c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\end{array}\right]$

cij= {2,se i=j i+j,se i≠j}

$c_{11} = 2 \\ c_{12} = 1+2 = 3 \\c_{13} = 1+3=4 \\c_{21}=2+1=3 \\c_{22}=2 \\c_{23} =2+3=5 \\ \\ C = \left[\begin{array}{ccc} 2 &3&4\\3&2&5\end{array}\right]$