EE-GATE_2014_S1_2 Marks

Question

A system matrix is given as follows.

A = $\begin{pmatrix} 0 & 1 &-1 \\ -6 &-11 &6 \\ -6 & -11 & 5 \end{pmatrix}$

The absolute value of the ratio of the maximum eigen value to the minimum eigen value is ?

Comments

I calculated the eigenvalues and they were -1, -2, -3.

Actually I'm confused whether to first take mod of eigenvalues and then consider them as maximum and minimum or first take maximum and minimum eigenvalue and then take mod of them to get answer.?

 

The actual answer as per key lies 2.9 to 3.1 and I wonder how can the answer be in decimal.

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Eigenvalues = -1, -2, -3

Max : -1   and    Min : -3

Their ratio = 1/3 and its absolute value also : 1/3 or 0.33