Question

Considere as matrizes A = (aij) e B (bij) quadradas de ordem 2, com aij = 3i + 4j e bij = -4i – 3j.

A) Construa as matrizes A e B.

B) Calcule A + 2.B - B​

Answer 1

A)

Matriz A:

$A = \left[ \begin{array}{cc}a_{1,1} & a_{1,2} \\ a_{2,1} & a_{2,2}\end{array} \right]$

$A = \left[ \begin{array}{cc} 3+4 & 3+8 \\ 6+4 & 6+8\end{array} \right]$

$A = \left[ \begin{array}{cc} 7& 11 \\ 10 & 14\end{array} \right]$

Matriz B:

$B = \left[ \begin{array}{cc}b_{1,1} & b_{1,2} \\ b_{2,1} & b_{2,2}\end{array} \right]$

$B = \left[ \begin{array}{cc}-4-3& -4-6 \\ -8-3 & -8-6\end{array} \right]$

$B = \left[ \begin{array}{cc}-7& -10 \\ -11 & -14\end{array} \right]$

B)

Chamemos a matriz resultante da soma A + 2.B - B de C. Temos que o termo cij de C será da forma:

$c_{i,j} = a_{i,j}+2\cdot b_{i,j} - b_{i,j}$

$c_{i,j} = a_{i,j}+b_{i,j}$

$c_{i,j} = 3i + 4j -4i - 3j$

$c_{i,j} = j-i$

Então C é igual a:

$C = \left[ \begin{array}{cc}c_{1,1} & c_{1,2} \\ c_{2,1} & c_{2,2}\end{array} \right]$

$C = \left[ \begin{array}{cc}1-1& 2-1 \\ 1-2 & 2-2\end{array} \right]$

$C = \left[ \begin{array}{cc}0& 1 \\ -1 & 0\end{array} \right]$