ExercĂcio Resolvido
Ălgebra Linear - Base e DimensĂŁo
O conjunto dos $(đ„_1,đ„_2,đ„_3,đ„_4)â â^4$ tais que $đ„_1+5đ„_2=5$ pode ser representado por:
a) $A=\left[
\begin{array}{c}
-10\\
3\\
1\\
-2 \\
\end{array}
\right]+ span \left\{ \left[\begin{array}{c} 0\\0\\-5\\1\\\end{array} \right], \left[\begin{array}{c}-6\\0\\0\\0\\\end{array} \right],\left[\begin{array}{c} 0\\4\\0\\0\\\end{array} \right] \right\}$
b) $A=\left[
\begin{array}{c}
20\\
-3\\
3\\
1\\
\end{array}
\right]+ span \left\{ \left[\begin{array}{c} 1\\-5\\0\\0\\\end{array} \right], \left[\begin{array}{c}0\\0\\-2\\0\\\end{array} \right],\left[\begin{array}{c} 0\\0\\0\\2\\\end{array} \right] \right\}$
c) $A=\left[
\begin{array}{c}
20\\
-3\\
3\\
1\\
\end{array}
\right]+ span \left\{ \left[\begin{array}{c} -5\\1\\0\\0\\\end{array} \right], \left[\begin{array}{c}0\\0\\-7\\0\\\end{array} \right],\left[\begin{array}{c} 0\\0\\0\\1\\\end{array} \right] \right\}$
d) $A=\left[
\begin{array}{c}
15\\
-3\\
-1\\
2\\
\end{array}
\right]+ span \left\{ \left[\begin{array}{c} -5\\1\\0\\0\\\end{array} \right], \left[\begin{array}{c}0\\0\\0\\3\\\end{array} \right],\left[\begin{array}{c} 0\\0\\-3\\0\\\end{array} \right] \right\}$
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