Question

dadas a matrizes A= 3 2 4 / 8 1 5​

Answer 1

Os resultados das somas de matrizes são:

a) $\left[\begin{array}{cc}2&1\\-1&-3\\8&10\\\end{array}\right]$

b) $\left[\begin{array}{cc}-2&-1\\1&3\\-8&-10\\\end{array}\right]$

c) $\left[\begin{array}{cc}4&8\\5&8\\8&7\\\end{array}\right]$

d) $\left[\begin{array}{cc}5&15\\8&12\\4&2\\\end{array}\right]$

Essa questão se trata de matrizes. Para responder essa questão, devemos considerar que:

• as matrizes são dadas na ordem mxn (m linhas e n colunas);

• a soma de matrizes só pode ser feita entre raízes de mesma ordem e o resultado é uma matriz cujos elementos é igual a soma dos respectivos elementos das outras matrizes;

a) Precisamos calcular A - B

$\left[\begin{array}{cc}3&8\\2&1\\4&5\\\end{array}\right] -\left[\begin{array}{cc}1&7\\3&4\\-4&-5\\\end{array}\right] =\left[\begin{array}{cc}3-1&8-7\\2-3&1-4\\4-(-4)&5-(-5)\\\end{array}\right] =\left[\begin{array}{cc}2&1\\-1&-3\\8&10\\\end{array}\right]$

b) Precisamos calcular B - A

$\left[\begin{array}{cc}1&7\\3&4\\-4&-5\\\end{array}\right] -\left[\begin{array}{cc}3&8\\2&1\\4&5\\\end{array}\right]=\left[\begin{array}{cc}1-3&7-8\\3-2&4-1\\-4-4&-5-5\\\end{array}\right] =\left[\begin{array}{cc}-2&-1\\1&3\\-8&-10\\\end{array}\right]$

c) Precisamos calcular A - C

$\left[\begin{array}{cc}3&8\\2&1\\4&5\\\end{array}\right] -\left[\begin{array}{cc}-1&0\\-3&-7\\-4&-2\\\end{array}\right] =\left[\begin{array}{cc}3-(-1)&8-0\\2-(-3)&1-(-7)\\4-(-4)&5-(-2)\\\end{array}\right] =\left[\begin{array}{cc}4&8\\5&8\\8&7\\\end{array}\right]$

d) Precisamos calcular A + B - C

$\left[\begin{array}{cc}3&8\\2&1\\4&5\\\end{array}\right]+\left[\begin{array}{cc}1&7\\3&4\\-4&-5\\\end{array}\right] -\left[\begin{array}{cc}-1&0\\-3&-7\\-4&-2\\\end{array}\right] =\left[\begin{array}{cc}3+1-(-1)&8+7-0\\2+3-(-3)&1+4-(-7)\\4+(-4)-(-4)&5+(-5)-(-2)\\\end{array}\right] =\left[\begin{array}{cc}5&15\\8&12\\4&2\\\end{array}\right]$