Respuesta :
Answer: a) AB = [tex]\left[\begin{array}{ccc}-14&26\\-11&22\end{array}\right][/tex] ; b) [tex]\left[\begin{array}{ccc}5&-5\\13&9\end{array}\right][/tex] ; c) No, they are different; d) No, they are never the same;
Step-by-step explanation:
a) A = [tex]\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right][/tex] , B = [tex]\left[\begin{array}{ccc}-2&1\\-3&7\end{array}\right][/tex]. This multiplication is possible, because matrix A has 2 columns and matrix B has 2 rows. When those value are equal, the multiplication is possible.
AB = [tex]\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}-2&1\\-3&7\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-14&26\\-11&22\end{array}\right][/tex]
b) BA = [tex]\left[\begin{array}{ccc}-2&1\\-3&7\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}-2&4\\1&3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5&-5\\13&9\end{array}\right][/tex]
c) As, we can see, parts a and b are differents.
d) With matrices, multiplication is not commutative, which means AB≠BA
Answer:
(a)[TeX]=\left(\begin{array}{cc}14 & 26\\7 & 22\end{array}\right) [/TeX]
(b)[Tex]\left(\begin{array}{cc}5 & -5\\1 & 33\end{array}\right) [/TeX]
(c)No
(d)AB≠BA
Step-by-step explanation:
[TeX]A= \left(\begin{array}{cc}-2 & 4\\1 & 3\end{array}\right) [/TeX]
[TeX]B= \left(\begin{array}{cc}-2 & 1\\3 & 7\end{array}\right)[/TeX]
(a)
[TeX] AB=\left(\begin{array}{cc}-2 & 4\\1 & 3\end{array}\right) \left(\begin{array}{cc}-2 & 1\\3 & 7end{array}\right)[/TeX]
[TeX]=\left(\begin{array}{cc}-2*-2+4*3 &-2*1+4*7\\1*-2+3*3 & 1*1+3*7\end{array}\right) [/TeX]
[TeX]=\left(\begin{array}{cc}14 & 26\\7 & 22\end{array}\right) [/TeX]
(b) [TeX]BA=\left(\begin{array}{cc}-2 & 1\\3&7\end{array}\right)\left(\begin{array}{cc}-2 & 4\\1 & 3\end{array}\right) [/TeX]
[TeX]=\left(\begin{array}{cc}-2*-2+1*1 & -2*4+1*3\\3*-2+7*1 &3*4+7*3\end{array}\right)=\left(\begin{array}{cc}5 & -5\\1 & 33\end{array}\right) [/TeX]
(c)No
(d)For Matrices A and B, AB≠BA.
Matrix Multiplication is not Commutative.
