Please help me solve this : If A²=2A-I, then for n≠2, A^n=?
Meghana Bhat , 8 Years ago
Grade 12
Algebra> Please help me solve this : If A²=2A-I, t...
1 Answers
Shahid
Given : A2 = 2A -I
To Find: An = ? ( n ≠ 2)
Solution:
A2 = 2A-I
A3 = A.A2 = A.(2A – I) = 2A2 – A = 2 (2A – I) – A = 4A – 2I – A = 3A – 2I
Similarly,
A4 = A. A3 = A.(3A – 2I) = 3A2 – 2A = 3 (2A – I) – 2A = 6A – 3I – 2A = 4A – 3I
… And so on...
Here , By Symmetry , We Observe That ,
An = nA – (n-1)I
Approved Last Activity: 8 Years ago
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