We show how the Cayley-Hamilton theorem can be used to give an expression for any power of a 2 by 2 matrix. The method is used to find the 4th power of a given matrix.

Powers of a 2 by 2 matrix (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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Powers of a 2 by 2 matrix (MathsCasts)

Powers of a 2 by 2 matrix (MathsCasts)