Question

Por favor me ajudem por favor isso e pra amanhã!!!
Dadas as matrizes A=3 0 1 -4 é B= 2 1 -1 o, então AB - BA a igual a: A= 0 0 0 0 B=2 -3 5 0 C=-3 1 2 7 D=1 0 0 1 E=-1 7 9 1​

Answer 1

$A=\left[\begin{array}{ccc}3&0\\1&-4\end{array}\right]$                    $B=\left[\begin{array}{ccc}2&1\\-1&0\end{array}\right]$

$A.B=\left[\begin{array}{ccc}3.2+0.(-1)&3.1+0.0\\1.2+(-4).(-1)&1.1+(-4).0\end{array}\right]=\left[\begin{array}{ccc}6+0&3+0\\2+4&1+0\end{array}\right]=\left[\begin{array}{ccc}6&3\\6&1\end{array}\right]$

$B.A=\left[\begin{array}{ccc}2.3+1.1&2.0+1.(-4)\\(-1).3+0.1&(-1).0+0.(-4)\end{array}\right]=\left[\begin{array}{ccc}6+1&0-4\\-3+0&0+0\end{array}\right]=\left[\begin{array}{ccc}7&-4\\-3&0\end{array}\right]$

$AB-BA=\left[\begin{array}{ccc}6&3\\6&1\end{array}\right]-\left[\begin{array}{ccc}7&-4\\-3&0\end{array}\right]=\left[\begin{array}{ccc}6-7&3-(-4)\\6-(-3)&1-0\end{array}\right]=\left[\begin{array}{ccc}-1&7\\9&1\end{array}\right]$