Question

state and prove cayley-hamilton theorem.​

Answer 1

Answer:

In linear algebra, the Cayley–Hamilton theorem states that every square matrix over a commutative ring satisfies its own characteristic equation.

Answer 2

Answer:

Its stated and proved in the explanation....

Step-by-step explanation:

In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex field) satisfies its own characteristic equation. ... The theorem holds for general quaternionic matrices.

The theorem allows An to be articulated as a linear combination of the lower matrix powers of A. If the ring is a field, the Cayley–Hamilton theorem is equal to the declaration that the smallest polynomial of a square matrix divided by its characteristic polynomial.

This theorem is used all over in linear algebra. One can easily find inverse of a matrix using Cayley Hamilton theorem. It also plays an important role in solving ordinary differential equations[2]. This theorem is quite useful in physics also.