Question

) If \( \left[\begin{array}{cc}x-y & 2 y \\ 2 y+z & x+y\end{array}\right]=\left[\begin{array}{ll}1 & 4 \\ 9 & 5\end{array}\right] \), find the value of \( x+y+z \)

Answer 1

x -  y = 1  ..... Eqn 1

2y  =  4   ..... Eqn 2

2y + z = 9  ..... Eqn 3

x + y = 5 ..... Eqn 4

From Eqn 2 ..... y = 2

From Eqn .. 1,     x = 1 + y =  3

From Eqn .. 3,      z = 9- 2y = 9 – 4 = 5

x + y + z = 3 + 2 + 5 = 10