Q55 of 307 Page 5

If find A2 – 5A + 4I and hence find a matrix X such that A2 – 5A + 4I + X = O.

Given.


We need to find A2 – 5A + 4I.


We know A2 = A × A.





Now, we evaluate –5A = –5 × A.





Finally, matrix 4I = 4 × I.





The given expression is A2 – 5A + 4I.





Given that A2 – 5A + 4I + X = O


⇒ X = – (A2 – 5A + 4I)




Thus, and


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