Question

verify cayley hamilton theorem and find its inverse of the following matrix [(1,4,1),(3,2,2),(7,3,1)]​

Answer 1

Answer:

To verify C- H theorem characteristic eqn |A- λI| =0

i.e. ∣∣∣∣1−λ−1023−λ−2−201−λ∣∣∣∣=0|1−λ2−2−13−λ00−21−λ|=0

Expanding we get a cubic equation in λ as λ3−5λ2+9λ−1=0λ3−5λ2+9λ−1=0

To verify C-H theorem we have to show that A3−5A2+9A−I=0A3−5A2+9A−I=0 ………………..(1)

Taking L.H.S. of eqn (1)

A3−5A2+9A–I=⎡⎣⎢−13−1110429−22−210−3⎤⎦⎥−5⎡⎣⎢−1−42127−8−421⎤⎦⎥+9⎡⎣⎢1−1023−2−201⎤⎦⎥−

Answer 2

Answer:

The answer is

A-1 = 1/8 [2/-6. -1/1]

is the correct answer

Thank you