Consider the system of equations `(a -1) x -y -z = 0` `x -(b -1) y +z = 0` `x + y - (c -1) z = 0` Where a, b and c are non-zero real number Statement1 : If x,y,z are not all zero, then `ab + bc + ca + abc` Statement 2 : `abc ge 27`A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 3B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 3C. Statement 1 is true, Statement 2 is FalseD. Statement 1 is False, Statement 2 is true

Consider the system of equations `(a -1) x -y -z = 0` `x -(b -1) y +z

1.	Consider the system of equations `(a -1) x -y -z = 0` `x -(b -1) y +z = 0` `x + y - (c -1) z = 0` Where a, b and c are non-zero real number Statement1 : If x,y,z are not all zero, then `ab + bc + ca + abc` Statement 2 : `abc ge 27`A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 3B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 3C. Statement 1 is true, Statement 2 is FalseD. Statement 1 is False, Statement 2 is true
Answer» Correct Answer - B It is given that x,y,z are not all zero. So, the given system of equation has a non-trivial solutions. `:. \|(a -1,-1,-1),(1,-(b -1),1),(1,1,-(c -1))\| = 0` `rArr \|(a,0,-1),(0,-b,1),(c,c,1-c)\| = 0 " " [("Applying " C_(1) rarr C_(1) - C_(3)),(C_(2) rarr C_(2) - C_(3))]` `rArr a(-b + bc -c) - (0 + bc) = 0` `rArr ab + bc + ac = abc` Using `A.M. ge G.M`., we have `(ab + bc + ca)/(3) ge (abc)^(2//3)` `rArr abc ge 3 (abc)^(2//3) rArr abc ge 27` So, both statements are true