Question

Cayley Hamilton theorem is verified for the matrix A = 0 0 1
L21-1
using​

Answer 1

Answer:

Cayley Hamilton theorem is verified for the matrix A = 0 0 1  L21-1  using​

3-by-3 matrix

Step-by-step explanation:

Cayley–Hamilton Theorem

One of the best-known properties of characteristic polynomials is that all square real or complex matrices satisfy their characteristic polynomials. This result is known as the Cayley–Hamilton theorem.

Illustration

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The Cayley–Hamilton theorem illustrated with a 3-by-3 matrix

characteristicPolynomialA = Det [A - t IdentityMatrix [3] ]

28 t + 3 t2 − t3

charPolyA =−MatrixPower [A, 3] + 3 MatrixPower [A, 2] + 28 A

{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}

This shows that the matrix A satisfies of its own characteristic polynomial.

Manipulation

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The Cayley–Hamilton illustrated with Manipulate

cpA = CharacteristicPolynomial[A, t]

− 12 + 3a + 2 4 t + at + 3 t2 − t3

Manipulate[Evaluate[− MatrixPower[A, 3] + 3 MatrixPower[A, 2] + (24 + a) A − (12 − 3 a) IdentityMatrix[3]], {a, − 5, 5, 1}]