For a vibrating system with ([k]=left[begin{array}{rr}2 & -1 -1 & 2end{array} ight]) and ([m]=left[begin{array}{ll}1 & 0

For a vibrating system with \([k]=\left[\begin{array}{rr}2 & -1 \\ -1 & 2\end{array}\right]\) and \([m]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), the mode shape closest to the fundamental mode, according to the Rayleigh's quotient, \(R(\vec{X})=\frac{\vec{X}^{T}[k] \vec{X}}{\vec{X}^{T}[m] \vec{X}}\), is given by

a. \(\vec{X}=\left\{\begin{array}{l}1 \\ 1\end{array}\right\}\)

b. \(\left\{\begin{array}{r}1 \\ -1\end{array}\right\}\)

c. \(\left\{\begin{array}{c}-1 \\ 1\end{array}\right\}\)