If matrix A = [[1, 1, 1], [1, 1, 1], [1, 1, 1]], then Aⁿ (where n is a positive integer) is equal to: A. n A B. 3ⁿ A C. 3^(n−1) A D. A Answer: C) 3^(n−1) A Explanation: A² = A × A = [[3, 3, 3], [3, 3, 3], [3, 3, 3]] = 3A. A³ = A² × A = 3A × A = 3A² = 3(3A) = 9A = 3²A. By induction, Aⁿ = 3^(n−1) A.

imo class 12 matrices

If matrix A = [[1, 1, 1], [1, 1, 1], [1, 1, 1]], then Aⁿ (where n is a positive integer) is equal to:

VAVidaara Admin Asked 6d ago 0 views 0 answers

If matrix A = [[1, 1, 1], [1, 1, 1], [1, 1, 1]], then Aⁿ (where n is a positive integer) is equal to:

Answer: C) 3^(n−1) A

Explanation: A² = A × A = [[3, 3, 3], [3, 3, 3], [3, 3, 3]] = 3A. A³ = A² × A = 3A × A = 3A² = 3(3A) = 9A = 3²A. By induction, Aⁿ = 3^(n−1) A.

No comments yet — start the discussion.