Q. 535.0( 3 Votes )

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Answer :

Given .

We need to find A2 – 5A – 14I.

We know A2 = A × A.    Now, we evaluate –5A = –5 × A.   Finally, matrix –14I = –14 × I.   The given expression is A2 – 5A – 14I.   On multiplying both sides with matrix A, we get

A (A2 – 5A – 14I) = O

A3 – 5A2 – 14(A × I) = O

A3 – 5A2 – 14A = O

A3 = 5A2 + 14A     Thus, and .

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