Question

Alguém me ajuda??? Matriz!!!

Answer 1

Bom dia

Temos $\left[\begin{array}{cc}4&5\\3&4\end{array}\right] \left[\begin{array}{ccc}x&y\\z&t\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

$\left \{ {{4x+5z=1} \atop {3x+4z=0}} \right. \\ \left \{ {{4y+5t=0} \atop {3y+4t=1}} \right.$

3x+4z=0⇒4z=-3x ⇒ z= (-3/4)x

4x+5z=1 ⇒ 4x+5*(-3/4)x=1⇒4x- (15/4)x=1 ⇒16x-15x=4 ⇒ x= 4

z= (-3/4)*4 ⇒z=-3

4y+5t=0 ⇒5t = -4y ⇒ t = (-4/5)y

3y+4t=1 ⇒ 3y + 4*(-4/5)y=1 ⇒ 3y- (16/5)y=1 ⇒15y-16y=5⇒-y=5⇒y= - 5

t=(-4/5)y ⇒ t= (-4/5)*(-5) ⇒ t=4

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