JEE Main202229 Jul 2022Evening ShiftMathematicsMatricesActual
Let x = 1 1 1 and A = - 1 2 3 0 1 6 0 0 - 1 . For k ∈ ℕ , if X ' A k X = 33 , then k is equal to
Correct answer
0
Step-by-step solution
Given, X = 1 1 1   &   A = - 1 2 3 0 1 6 0 0 - 1 Also given, X T A K X = 33 Now putting the value of matrices in X T A K X = 33 we get, 1 1 1 - 1 2 3 0 1 6 0 0 - 1 k 1 1 1 = 33 Now finding A 2 = - 1 2 3 0 1 6 0 0 - 1 - 1 2 3 0 1 6 0 0 - 1 = 1 0 6 0 1 0 0 0 1 And A 4 = 1 0 6 0 1 0 0 0 1 1 0 6 0 1 0 0 0 1 = 1 0 12 0 1 0 0 0 1 Similary A 8 = 1 0 24 0 1 0 0 0 1 And A 10 = 1 0 6 0 1 0 0 0 1 1 0 24 0 1 0 0 0 1 = 1 0 30 0 1 0 0 0 1 So, for K → Even A K = 1 0 3 K 0 1 0 0 0 1 Now again putting the value