Question

Sabendo que a matriz A 3x3 onde AIJ = 3i + 2j e uma matriz B 3x3 onde bij = 2i - j ?
Calcule a Matriz A-B

Answer 1

Resposta:

Explicação passo-a-passo:

Determinando as matrizes:

$A_{3x3}$

$A_{ij} = 3i + 2j$

Assim:

$A_{11} = 3(1)+2(1) = 5\\A_{12} = 3(1) + 2(2) = 7\\A_{13} = 3(1) + 2(3) = 9\\A_{21} = 3(2) + 2(1) = 8\\A_{22} = 3(2) + 2(2) = 10\\A_{23} = 3(2) + 2(3) = 12\\A_{31} = 3(3) + 2(1) = 11\\A_{32} = 3(3) + 2(2) = 13\\A_{33} = 3(3) + 2(3) = 15$

$A = \left[\begin{array}{ccc}5&7&9\\8&10&12\\11&13&15\end{array}\right]$

A outra matriz:

$B_{3x3}\\B_{ij}= 2i-j$

$B_{11} = 2(1) -1 = 1\\B_{12} = 2(1) - 2 = 0\\B_{13}=2(1) - 3 = -1\\B_{21} = 2(2) - 1 =3\\B_{22} = 2(2) -2 = 2\\B_{23} = 2(2) - 3 = 1\\B_{31} = 2(3) - 1 = 5\\B_{32} = 2(3) -2 = 4\\B_{33} = 2(3) - 3 = 3$

$B = \left[\begin{array}{ccc}1&0&-1\\3&2&1\\5&4&3\end{array}\right]$

Assim:

$A-B = \left[\begin{array}{ccc}5-1&7-0&9-(-1)\\8-3&10-2&12-1\\11-5&13-4&15-3\end{array}\right]$

$A-B = \left[\begin{array}{ccc}4&7&10\\5&8&11\\6&9&12\end{array}\right]$