Question

Daing. Cayley-Harmilton
theorem
find the inverse of the matrix
2 3
3 5
S 12​

Answer 1

Answer:

experiment - verification of the ohm law using a simple electric circuit. Daing. Cayley-Harmilton

theorem

find the inverse of the matrix

2 3

3 5

S 12

Answer 2

Answer:

n 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 Cayley–Hamilton theorem states that this polynomial results in the zero matrix, which is to say that {\displaystyle p(A)=\mathbf {0} }{\displaystyle p(A)=\mathbf {0} }. The theorem allows An to be expressed as a linear combination of the lower matrix powers of A. When the ring is a field, the Cayley–Hamilton theorem is equivalent to the statement that the minimal polynomial of a square matrix divides its characteristic polynomial. The theorem was first proved in 1853[8] in terms of inverses of linear functions of quaternions, a non-commutative ring, by Hamilton.[4][5][6] This corresponds to the special case of certain 4 × 4 real or 2 × 2 complex matrices. The theorem holds for general quaternionic matrices.[9][nb 1] Cayley in 1858 stated it for 3 × 3 and smaller matrices, but only published a proof for the 2 × 2 case.[2] The general case was first proved by Frobenius in 1878.[10]

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