Preciso de escrever uma matriz (aij) 2x3 tal que aij =i² - j²?
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Boa noite Pamela!
Solução!
Primeiro escrevemos a matriz na sua forma algébrica.
A lei que define os valores numéricos da matriz!
![a11=i^{2}-j^{2}~~\Rightarrow~~a11=1^{2} -1^{2} =0\\\\\\
a12=i^{2}-j^{2}~~\Rightarrow~~a12=1^{2}-2^{2}=-3 \\\\\\\
a13=i^{2}-j^{2}~~\Rightarrow~~a13=1^{2}-3^{2}=-8 \\\\\\\\\\\\\
a21=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-1^{2}=3\\\\\\\
a22=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-2^{2}=0\\\\\\\
a23=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-3^{2}=-5\\\\\\\](https://tex.z-dn.net/?f=a11%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea11%3D1%5E%7B2%7D+-1%5E%7B2%7D+%3D0%5C%5C%5C%5C%5C%5C%0Aa12%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea12%3D1%5E%7B2%7D-2%5E%7B2%7D%3D-3++%5C%5C%5C%5C%5C%5C%5C%0Aa13%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea13%3D1%5E%7B2%7D-3%5E%7B2%7D%3D-8++%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0Aa21%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea21%3D2%5E%7B2%7D-1%5E%7B2%7D%3D3%5C%5C%5C%5C%5C%5C%5C%0Aa22%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea21%3D2%5E%7B2%7D-2%5E%7B2%7D%3D0%5C%5C%5C%5C%5C%5C%5C%0Aa23%3Di%5E%7B2%7D-j%5E%7B2%7D%7E%7E%5CRightarrow%7E%7Ea21%3D2%5E%7B2%7D-3%5E%7B2%7D%3D-5%5C%5C%5C%5C%5C%5C%5C%0A++++++++++ "a11=i^{2}-j^{2}~~\Rightarrow~~a11=1^{2} -1^{2} =0\\\\\\
a12=i^{2}-j^{2}~~\Rightarrow~~a12=1^{2}-2^{2}=-3 \\\\\\\
a13=i^{2}-j^{2}~~\Rightarrow~~a13=1^{2}-3^{2}=-8 \\\\\\\\\\\\\
a21=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-1^{2}=3\\\\\\\
a22=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-2^{2}=0\\\\\\\
a23=i^{2}-j^{2}~~\Rightarrow~~a21=2^{2}-3^{2}=-5\\\\\\\")
A matriz procurada é:
![A=\begin{pmatrix} 0 & -3&-8\\ 3 &0&-5 \\ \end{pmatrix}\\\\\\\\\\\
\boxed{Resposta:A=\begin{pmatrix} 0 & -3&-8\\ 3 &0&-5 \\ \end{pmatrix}}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bpmatrix%7D+0+%26amp%3B+-3%26amp%3B-8%5C%5C+3+%26amp%3B0%26amp%3B-5+%5C%5C+%5Cend%7Bpmatrix%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3AA%3D%5Cbegin%7Bpmatrix%7D+0+%26amp%3B+-3%26amp%3B-8%5C%5C+3+%26amp%3B0%26amp%3B-5+%5C%5C+%5Cend%7Bpmatrix%7D%7D "A=\begin{pmatrix} 0 & -3&-8\\ 3 &0&-5 \\ \end{pmatrix}\\\\\\\\\\\
\boxed{Resposta:A=\begin{pmatrix} 0 & -3&-8\\ 3 &0&-5 \\ \end{pmatrix}}")
Boa noite!
Bons estudos!
Solução!
Primeiro escrevemos a matriz na sua forma algébrica.
A lei que define os valores numéricos da matriz!
A matriz procurada é:
Boa noite!
Bons estudos!
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