GATE Civil Engineering
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The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are

  1. $1.55$ and $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$
  1. $2.00$ and $\begin{Bmatrix} 1.00\\ 1.00 \end{Bmatrix}$
  1. $1.55$ and $\begin{Bmatrix} -2.55\\ -0.45 \end{Bmatrix}$
  1. $1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$
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