Question

Dada as matrizes $A= \left[\begin{array}{ccc}x+y&3\\0&2\\2&4\end{array}\right]$ , $B = \left[\begin{array}{ccc}1&2\\x-y&4\end{array}\right]$ e $C= \left[\begin{array}{ccc}10&14\\6&8\\14&20\end{array}\right]$ determine os valores de x e y para que A . B = C.

Answer 1

$(x+y,3)\cdot(1,x-y)=10\iff 4x-2y=10\\ (x+y,3)\cdot(2,4)=10\iff 2(x+y)+12=10\iff x+y=-1\\ \\ \begin{cases} 4x-2y=10\\ x+y=-1 \end{cases}\\ \\ \\ \boxed{x=\dfrac{4}{3}\wedge y=-\dfrac{7}{3}}$