Question

Será que alguém poderia me ajudar com esse exercício de matrizes?

Answer 1

1.

Matriz J

$\left[\begin{array}{cc}3&5\\4&6\end{array}\right]$

Matriz K

$\left[\begin{array}{cc}1&0\\3&2\end{array}\right]$

a) Matriz J + K

$\left[\begin{array}{cc}3&5\\4&6\end{array}\right]+ \left[\begin{array}{cc}1&0\\3&2\end{array}\right] = \left[\begin{array}{cc}4&5\\7&8\end{array}\right]$

b) Matriz J - K

$\left[\begin{array}{cc}3&5\\4&6\end{array}\right] - \left[\begin{array}{cc}1&0\\3&2\end{array}\right] = \left[\begin{array}{cc}2&5\\1&4\end{array}\right]$

2.

a) M - N = P

$\left[\begin{array}{ccc}2&-1&0\\-3&1&3\\0&-2&1\end{array}\right] - \left[\begin{array}{ccc}5&-1&2\\1&-2&-3\\3&-4&2\end{array}\right] = \left[\begin{array}{ccc}-3&0&-2\\-4&3&6\\-3&2&-1\end{array}\right]$

b) M + N = Q

$\left[\begin{array}{ccc}2&-1&0\\-3&1&3\\0&-2&1\end{array}\right] + \left[\begin{array}{ccc}5&-1&2\\1&-2&-3\\3&-4&2\end{array}\right] = \left[\begin{array}{ccc}7&-2&2\\-2&-1&0\\3&-6&3\end{array}\right]$

c) (N - M )¹ = O

$\left[\begin{array}{ccc}5&-1&2\\1&-2&-3\\3&-4&2\end{array}\right] - \left[\begin{array}{ccc}2&-1&0\\-3&1&3\\0&-2&1\end{array}\right] = \left[\begin{array}{ccc}3&0&2\\4&-3&-6\\3&-2&1\end{array}\right]$

3.

Se Matriz A = Matriz B

$\left[\begin{array}{cc}x^{2}&1\\1&3y - 1\end{array}\right] = \left[\begin{array}{cc}4&1\\1&2\end{array}\right]$

Então

$x^{2} = 4\\ x_{1} = 2\\ x_{2} = -2 \\ \\ 3y-1 = 2\\ 3y = 3\\ y = 1$

Resposta c)