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 x^ 2 +x & x+1 & x-2 \\ 2 x^ 2 +3 x-1 & 3 x & 3 x-3 \\ x^ 2 +2 x+3 & 2 x-1 & 2 x-1 array |= p x+ q , then p ^ 2 =196 q ^ 2 ,
B. both are false
Statement I: Let D_1 = vmatrix 1 & & \\ & 1 & \\ & & 1 vmatrix = 1 - ^2 - ^2 - ^2 + 2 . D_2 = vmatrix 0 & & \\ & 0 & \\ & & 0 vmatrix = 2 . D_1 = D_2 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.
Related: Mathematics — Determinants · All PYQ Banks