Q8 of 26 Page 1

Let , then show that A2 – 4A + 7I = O.

Using this result calculate A3 also.


OR


If , find A-1 , using elementary row operations.


Given:


To show: A2 – 4A + 7I = O and also find A3


Proof:


Firstly, we calculate A2






Putting the value in given equation, we get


A2 – 4A + 7I







= 0


= RHS


Now, we have to find the A3






OR


Given:


We know that, A = IA



R2→ R2 – 2R1




R3→ 3R3




R3→ R3 – R2




R1→ R1 – R3




R2→ R2 + 7R3







R3↔ R2



R2→ -R2




This is similar to


I = A-1A


Hence,


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