GATE (TF) Textile 2019 Question Paper Solution | GATE/2019/TF/03

The eigenvalues of the matrix $\begin{pmatrix} 3 & 0 & 0\\ 0 & 2 & -3\\ 0 & 1 & -2 \end{pmatrix}$ are

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A= $\begin{pmatrix} 3 & 0 & 0\\ 0 & 2 & -3\\ 0 & 1 & -2 \end{pmatrix}$

$A-\lambda \times I=0$

$\begin{pmatrix} 3 & 0 & 0\\ 0 & 2 & -3\\ 0 & 1 & -2 \end{pmatrix}-\lambda \times \begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}=0$

$\begin{pmatrix} 3-\lambda & 0 & 0\\ 0 & 2-\lambda & -3\\ 0 & 1 & -2-\lambda \end{pmatrix}=0$

$(3-\lambda)[(2-\lambda)(-2-\lambda)+3]-0+0=0$

$(3-\lambda)[(-4+\lambda^2)+3]=0$

$(3-\lambda)[\lambda^2-1]=0$

$\lambda=3 , 1 , -1$ (Ans)

These are the eigen values.