If \(\begin{bmatrix} x+y+z\\x+z \\ y + z\end{bmatrix} = \begin{bmatrix} 11\\6 \\ 8\end{bmatrix} \) then the value of x + 2y - 3z is
Answer & explanation
Correct answer: option 2
x + y + z = 11 ....(i)
x + z = 6 ....(ii)
y + z = 8 ....(iii)
Subtraction eq. (ii) form (iii)
y + z - (x + z) = 8 - 6
⇒ y + z - x - z = 2
⇒ y - x = 2
⇒ y = 2 + x
Putting y in eq. (i)
x + (2 + x) + z = 11
x + 2x + z = 11
2x + z = 11 - 2
2x + z = 9 ....(iv)
Subtraction eq. (iii) form (iv)
2x + z -(x + z) = 9 - 6
2x + z - x - z = 3
2x - x = 3
x = 3
y = 2 + x
y = 2 + 3 = 5
Put value of x in eq. (ii)
x + z = 6
3 + z = 6 ⇒ z = 6 - 3 = 3
So, according to question x + 2y - 3z ⇒ 3 + 2 × (5) - 393)
= 3 + 10 - 9 = 3 + 1 = 4