Among the statements : I: If | array ccc 1 & & & 1 & & & 1 array |= | array ccc 0 & & & 0 & & & 0 array | , then ² + ² + ² = 3 2 , and II : If | array ccc x²+x & x+1 & x-2 2 x²+3 x-1 & 3 x & 3 x-3 x²+2 x+3 & 2 x-1 & 2 x-1 array |= p x+ q , then p ²=196 q ² ,

Step-by-step solution

Statement I: Let D₁ = vmatrix 1 & & & 1 & & & 1 vmatrix = 1 - ^2 - ^2 - ^2 + 2 . D₂ = vmatrix 0 & & & 0 & & & 0 vmatrix = 2 . D₁ = D₂ 1 - ^2 - ^2 - ^2 = 0 ^2 + ^2 + ^2 = 1 3 2 . Statement I is false. Statement II: Evaluate by substituting x = 0 : determinant = -12 , so q = -12 . At x = 1 : determinant = 12 , so p + q = 12 p = 24 . p^2 = 576 and 196q^2 = 196 144 = 28224 . Since p^2 196q^2 , Statement II is false. Both statements are false.