Escreva a matriz A3x3 cujos elementos
aij são definidos por:
aij= { i+j se i < j
0 se i = j
i elevado a j se i > j
Respostas
respondido por:
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Olá, Caputigarcia.
![a_{11}=0,\text{pois }i=j\\a_{12}=1+2=3,\text{pois }i\ \textless \ j\\a_{13}=1+3=4,\text{pois }i\ \textless \ j\\
a_{21}=2^1=2,\text{pois }i\ \textgreater \ j\\a_{22}=0,\text{pois }i=j\\a_{23}=2+3=5,\text{pois }i\ \textless \ j\\
a_{31}=3^1=3,\text{pois }i\ \textgreater \ j\\a_{32}=3^2=9,\text{pois }i\ \textgreater \ j\\a_{33}=0,\text{pois }i=j
\\\\
\therefore\boxed{A= \left[\begin{array}{ccc}0&3&4\\2&0&5\\3&9&0\end{array}\right] }](https://tex.z-dn.net/?f=a_%7B11%7D%3D0%2C%5Ctext%7Bpois+%7Di%3Dj%5C%5Ca_%7B12%7D%3D1%2B2%3D3%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextless+%5C+j%5C%5Ca_%7B13%7D%3D1%2B3%3D4%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextless+%5C+j%5C%5C%0Aa_%7B21%7D%3D2%5E1%3D2%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextgreater+%5C+j%5C%5Ca_%7B22%7D%3D0%2C%5Ctext%7Bpois+%7Di%3Dj%5C%5Ca_%7B23%7D%3D2%2B3%3D5%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextless+%5C+j%5C%5C%0Aa_%7B31%7D%3D3%5E1%3D3%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextgreater+%5C+j%5C%5Ca_%7B32%7D%3D3%5E2%3D9%2C%5Ctext%7Bpois+%7Di%5C+%5Ctextgreater+%5C+j%5C%5Ca_%7B33%7D%3D0%2C%5Ctext%7Bpois+%7Di%3Dj%0A%5C%5C%5C%5C%0A%5Ctherefore%5Cboxed%7BA%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B3%26amp%3B4%5C%5C2%26amp%3B0%26amp%3B5%5C%5C3%26amp%3B9%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+%7D "a_{11}=0,\text{pois }i=j\\a_{12}=1+2=3,\text{pois }i\ \textless \ j\\a_{13}=1+3=4,\text{pois }i\ \textless \ j\\
a_{21}=2^1=2,\text{pois }i\ \textgreater \ j\\a_{22}=0,\text{pois }i=j\\a_{23}=2+3=5,\text{pois }i\ \textless \ j\\
a_{31}=3^1=3,\text{pois }i\ \textgreater \ j\\a_{32}=3^2=9,\text{pois }i\ \textgreater \ j\\a_{33}=0,\text{pois }i=j
\\\\
\therefore\boxed{A= \left[\begin{array}{ccc}0&3&4\\2&0&5\\3&9&0\end{array}\right] }")
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