Question

seja A,B e C matrizes de ordem 2x3 tal que,aij=2i+j,bij=3j e cij=2i - 3j.calcule:

A) B-A
B)A - C
C) 2A -(B+C)
D) 4C -3B

Answer 1

Matriz A = $\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\end{array}\right]$
Matriz A = $\left[\begin{array}{ccc}2.1+1&2.1+2&2.1+3\\2.2+1&2.2+2&2.2+3\end{array}\right]$
Matriz A = $\left[\begin{array}{ccc}3&4&5\\5&6&7\end{array}\right]$

Matriz B = $\left[\begin{array}{ccc}b11&b12&b13\\b21&b22&b23\end{array}\right]$
Matriz B = $\left[\begin{array}{ccc}3.1&3.2&3.3\\3.1&3.2&3.3\end{array}\right]$
Matriz B = $\left[\begin{array}{ccc}3&6&9\\3&6&9\end{array}\right]$

Matriz C = $\left[\begin{array}{ccc}c11&c12&c13\\c21&c22&c23\end{array}\right]$
Matriz C = $\left[\begin{array}{ccc}2.1-3.1&2.1-3.2&2.1-3.3\\2.2-3.1&2.2-3.2&2.2-3.3\end{array}\right]$
Matriz C = $\left[\begin{array}{ccc}-1&-4&-7\\1&-2&-5\end{array}\right]$

A) Matriz B - Matriz A
     = $\left[\begin{array}{ccc}3&6&9\\3&6&9\end{array}\right]$ - $\left[\begin{array}{ccc}3&4&5\\5&6&7\end{array}\right]$
     = $\left[\begin{array}{ccc}0&2&4\\-2&0&2\end{array}\right]$

B) Matriz A - Matriz C
     = $\left[\begin{array}{ccc}3&4&5\\5&6&7\end{array}\right]$ - $\left[\begin{array}{ccc}-1&-4&-7\\1&-2&-5\end{array}\right]$
     = $\left[\begin{array}{ccc}4&8&12\\4&8&12\end{array}\right]$

C) 2.Matriz A - (Matriz B + Matriz C)
     = 2.$\left[\begin{array}{ccc}3&4&5\\5&6&7\end{array}\right]$ - ($\left[\begin{array}{ccc}3&6&9\\3&6&9\end{array}\right]$ + $\left[\begin{array}{ccc}-1&-4&-7\\1&-2&-5\end{array}\right]$)
     = $\left[\begin{array}{ccc}6&8&10\\10&12&14\end{array}\right]$ - $\left[\begin{array}{ccc}2&2&2\\4&4&4\end{array}\right]$
     = $\left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right]$

D) 4.Matriz C - 3.Matriz B
     = 4.$\left[\begin{array}{ccc}-1&-4&-7\\1&-2&-5\end{array}\right]$ - 3.$\left[\begin{array}{ccc}3&6&9\\3&6&9\end{array}\right]$
     = $\left[\begin{array}{ccc}-4&-16&-28\\4&-8&-10\end{array}\right]$ - $\left[\begin{array}{ccc}9&18&27\\9&18&27\end{array}\right]$
     = $\left[\begin{array}{ccc}-13&-34&-55\\-5&-26&-37\end{array}\right]$