Question

For the equation, \[ \begin{array}{r} {\left[\begin{array}{lll} x & 2 y & 3 z \end{array}\right]-2\left[\begin{array}{lll} y & z & -x \end{array}\right]+3\left[\begin{array}{lll} -z & x & -y \end{array}\right]} \\ =\left[\begin{array}{lll} 3 & 1 & 5 \end{array}\right] \end{array} \] then the value of \( x+y+z \) (a) 0 (b) 1 (c) -1 (d) 2

Answer 1

x-2y-3z = 3   Eqn 1

3x+2y-2z = 1  Eqn 2

2x -3y +3z = 5  Eqn 3

Eliminating x from  Eqn 1 and 2

8y + 7z = -8   Eqn 4

Eliminating x from  Eqn 1 and 3

y + 9z = -1   Eqn 5

Solving Eqn 4 and 5

z = 0, y = -1  

from Eqn 1 .... x = 1

x + y + z = 1 - 1 + 0 = 0