Question

Seja a matriz A = (aij) 2x3 , em que aij = 3i -2j . Que alternativa representa a matriz At ?

Answer 1

Boa tarde!

Matriz:

$\begin{bmatrix}a11&a12&a13\\a21&a22&a23\\\end{bmatrix}$

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$a11\Rightarrow\mathrm{3\times1}-\mathrm{2\times1}\Rightarrow\mathrm{3-2}=\boxed{\boxed{1}}$

$a12\Rightarrow\mathrm{3\times1}-\mathrm{2\times2}\Rightarrow\mathrm{3-4}=\boxed{\boxed{-1}}$

$a13\Rightarrow\mathrm{3\times1}-\mathrm{2\times3}\Rightarrow\mathrm{3-6}=\boxed{\boxed{-3}}$

$a21\Rightarrow\mathrm{3\times2}-\mathrm{2\times1}\Rightarrow\mathrm{6-2}=\boxed{\boxed{4}}$

$a22\Rightarrow\mathrm{3\times2}-\mathrm{2\times2}\Rightarrow\mathrm{6-4}=\boxed{\boxed{2}}$

$a23\Rightarrow\mathrm{3\times2}-\mathrm{2\times3}\Rightarrow\mathrm{6-6}=\boxed{\boxed{0}}$

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Matriz resposta:

$\begin{bmatrix}1&-1&-3\\4&2&0\\\end{bmatrix}$

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Matriz Transposta: (sua resposta)

$\mathrm{a}^{t}=\begin{bmatrix}1&4\\-1&2\\-3&0\\\end{bmatrix}$

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Att;Guilherme Lima