GATE 2018 | MATHS | Q-23

Question

Let A = A = \begin{bmatrix}
a & 2f & 0 \\
2f & b & 3f \\
0 & 3f & c \\
\end{bmatrix}
, where $a, b, c, f$ are real numbers and $f  not equalto0$. The geometric multiplicity of the largest eigenvalue of A equals ._______