Question

If a 3X3 matrix M has characteristic equation 1lambda^3 -39lambda^2 + 5lambda = 0. What is the value of the larger non-zero eigenvalue of M? It is not required to know M exactly. Give your answer to 3 decimal places

Answer 1

38.8713

Explanation:

We have given the a 3×3 matrix

The characteristic equation of the matrix is given by
`\lambda ^3-39\lambda ^2+5\lambda =0`

This is the property of the characteristic equation that the root of the the characteristic equation are the eigen value of the matrix

The roots of the equation
`\lambda ^3-39\lambda ^2+5\lambda =0` are
`\lambda =38.8713\ \lambda =0\ \lambda =0.12863`

We have to find the larger non zero eigen value

So the larger non zero eigen value will be 38.8713