Engineering Board Exam Reviewer · Matrix Operations · hard

Given A= bmatrix1&1\1&0 bmatrix, find A10.

1. bmatrix55&34\34&21 bmatrix
2. bmatrix144&89\89&55 bmatrix
3. bmatrix10&10\10&0 bmatrix
4. bmatrix89&55\55&34 bmatrix

Answer

D. bmatrix89&55\55&34 bmatrix

Solution

The powers of A generate Fibonacci numbers: An= bmatrixFn+1&Fn n&Fn-1 bmatrix. With F9=34, F10=55, F11=89: A10= bmatrix89&55\55&34 bmatrix.

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