Question

URGENTE, POR FAVOR

sendo A = (aij)2x2, onde aij = 2i - j, e B = (bij)2x2, com bij = j - i, determine
a) 4A
b) A-B
c) Bt
d)2A-Ae
e) a11 b11
f) a 22 b 12

Answer 1

`\mathbf A=\begin{bmatrix}a_(1,1)&a_(1,2)\\a_(2,1)&a_(2,2)\end{bmatrix}`


`a_(i,j)=2i-j\implies\mathbf A=\begin{bmatrix}2\cdot1-1&2\cdot1-2\\2\cdot2-1&2\cdot2-2\end{bmatrix}=\begin{bmatrix}1&0\\3&2\end{bmatrix}`

Por la misma razón,


`\mathbf B=\begin{bmatrix}1-1&2-1\\1-2&2-2\end{bmatrix}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}`

Entonces,


`4\mathbf A=\begin{bmatrix}4\cdot1&4\cdot0\\4\cdot3&4\cdot2\end{bmatrix}=\begin{bmatrix}4&0\\12&8\end{bmatrix}`


`\mathbf A-\mathbf B=\begin{bmatrix}1&0\\3&2\end{bmatrix}-\begin{bmatrix}0&1\\-1&0\end{bmatrix}=\begin{bmatrix}1-0&0-1\\3-(-1)&2-0\end{bmatrix}=\begin{bmatrix}1&-1\\4&2\end{bmatrix}`


`\mathbf B^\top=(b_(j,i))_(2*2)=\begin{bmatrix}b_(1,1)&b_(2,1)\\b_(1,2)&b_(2,2)\end{bmatrix}=\begin{bmatrix}0&-1\\1&0\end{bmatrix}`

Yo no reconozco la notación "Ae"... Puedes explicarla?


`a_(1,1)\cdot b_(1,1)=1\cdot0=0`


`a_(2,2)\cdot b_(1,2)=2\cdot1=2`