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[tex]Quest\~ao\ 02:[/tex]

[tex]A=\left[\begin{array}{cc}2&1\\3&1\end{array}\right] \ e\ B=\left[\begin{array}{cc}3&4\\1&0\end{array}\right][/tex]

[tex]A)\ \ A.B[/tex]

[tex]C_{11}= 2\times3+1\times 1=6+1=7\\C_{12}= 2\times4+1\times 0=8+0=8\\C_{21}= 3\times3+1\times 1=9+1=10\\C_{22}= 3\times4+1\times 0=12+0=12[/tex]

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[tex]A.B=\left[\begin{array}{cc}7&8\\10&12\end{array}\right][/tex]

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[tex]B)\ \ B.A[/tex]

[tex]C_{11}= 3\times2+4\times 3=6+12=18\\C_{12}= 3\times1+4\times 1=3+4=7\\C_{21}= 1\times2+0\times 3=2+0=2\\C_{22}= 1\times1+0\times 1=1+0=1[/tex]

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[tex]B.A=\left[\begin{array}{cc}18&7\\2&1\end{array}\right][/tex]

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[tex]C)\ \ A.B=B.A[/tex]

[tex]\left[\begin{array}{cc}7&8\\10&12\end{array}\right]=\left[\begin{array}{cc}18&7\\2&1\end{array}\right]\ \ \ \Leftarrow\ \ Falso.[/tex]

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[tex]Quest\~ao\ 03:[/tex]

[tex]A=\left[\begin{array}{cc}3&1\\4&-1\end{array}\right] \ e\ B=\left[\begin{array}{cc}2&1\\0&5\end{array}\right][/tex]

[tex]A)\ \ A.B[/tex]

[tex]C_{11}= 3\times2+1\times 0=6+0=6\\C_{12}= 3\times1+1\times 5=3+5=8\\C_{21}= 4\times2+(-1)\times 0=8-0=8\\C_{22}= 4\times1+(-1)\times 5=4-5=-1[/tex]

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[tex]A.B=\left[\begin{array}{cc}6&8\\8&-1\end{array}\right][/tex]

[tex]---------------------[/tex]

[tex]B)\ \ B.A[/tex]

[tex]C_{11}= 2\times3+1\times 4=6+4=10\\C_{12}= 2\times1+1\times (-1)=2-1=1\\C_{21}= 0\times3+5\times 4=0+20=20\\C_{22}= 0\times1+5\times (-1)=0-5=-5[/tex]

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[tex]B.A=\left[\begin{array}{cc}10&1\\20&-5\end{array}\right][/tex]

[tex]---------------------[/tex]

[tex]C)\ \ A.B=B.A[/tex]

[tex]\left[\begin{array}{cc}6&8\\8&-1\end{array}\right]=\left[\begin{array}{cc}10&1\\20&-5\end{array}\right]\ \ \ \Leftarrow\ \ Falso.[/tex]