Question

Sendo as matrizes

A=(2 4 5 -6)
B=(-2 6 -1 3) e
C=(5 6 2 0),

Determine:

A) A+2B -C
B) 2A -3C​

Answer 1

a)

$A~+~2B~-~C~=\\\\\\=~\left[\begin{array}{ccc}2&4\\5&-6\end{array}\right]+2\,.\,\left[\begin{array}{ccc}-2&6\\-1&3\end{array}\right]-\left[\begin{array}{ccc}5&6\\2&0\end{array}\right]\\\\\\\\=~\left[\begin{array}{ccc}2&4\\5&-6\end{array}\right]+\left[\begin{array}{ccc}-4&12\\-2&6\end{array}\right]-\left[\begin{array}{ccc}5&6\\2&0\end{array}\right]$

$=~\left[\begin{array}{ccc}2+(-4)-5~&~4+12-6\\5+(-2)-2~&~-6+6-0\end{array}\right]\\\\\\\\=~\left[\begin{array}{ccc}-7&10\\1&0\end{array}\right]$

b)

$2A~+~3C~=\\\\\\=~2\,.\,\left[\begin{array}{ccc}2&4\\5&-6\end{array}\right]-3\,.\,\left[\begin{array}{ccc}5&6\\2&0\end{array}\right]\\\\\\\\=~\left[\begin{array}{ccc}4&8\\10&-12\end{array}\right]-\left[\begin{array}{ccc}15&18\\6&0\end{array}\right]$

$=~\left[\begin{array}{ccc}4-15~&~8-18\\10-6~&~-12-0\end{array}\right]-\left[\begin{array}{ccc}15&18\\6&0\end{array}\right]\\\\\\\\=~\left[\begin{array}{ccc}-11&-10\\4&-12\end{array}\right]$

Answer 2

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