Question

sabendo-se que a matriz

A=(-3. 2)(-5. 1) e amatriz B=(2. 6)(4. 10), calcule o valor de 3A+B^2

Answer 1

Olá!

Temos os seguintes dados:

$A = \left[\begin{array}{cc}-3&2\\-5&1\\\end{array}\right]$

$B = \left[\begin{array}{cc}2&6\\4&10\\\end{array}\right]$

Vamos, calcular o valor de 3A + B², sabemos que B² = B*B, então:

$3*\left[\begin{array}{cc}-3&2\\-5&1\\\end{array}\right] + \left[\begin{array}{cc}2&6\\4&10\\\end{array}\right] *\left[\begin{array}{cc}2&6\\4&10\\\end{array}\right] = ?$

$\left[\begin{array}{cc}-9&6\\-15&3\\\end{array}\right] + \left[\begin{array}{cc}2*2+6*4&2*6+6*10\\4*2+10*4&4*6+10*10\\\end{array}\right] =$

$\left[\begin{array}{cc}-9&6\\-15&3\\\end{array}\right] + \left[\begin{array}{cc}4+24&12+60\\8+40&24+100\\\end{array}\right] =$

$\left[\begin{array}{cc}-9&6\\-15&3\\\end{array}\right] + \left[\begin{array}{cc}28&72\\48&124\\\end{array}\right] =$

$= \left[\begin{array}{cc}19&78\\33&127\\\end{array}\right] \end{array}}\qquad\checkmark$

Espero ter ajudado! =)