(Solved): Given stiffness matrix \( [\mathbf{K}] \) and mass matrix \( [\mathbf{M}] \) ...

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Given stiffness matrix \( [\mathbf{K}] \) and mass matrix \( [\mathbf{M}] \) as below; \[ \begin{array}{l} {[\boldsymbol{K}]=\left[\begin{array}{llll} 4 & 3 & 2 & 0 \\ 3 & 3 & 1 & 0 \\ 2 & 1 & 2 & 1 \\ 0 & 0 & 1 & 4 \end{array}\right]} \\ {[\boldsymbol{M}]=\left[\begin{array}{llll} 3 & 1 & 2 & 0 \\ 1 & 2 & 1 & 0 \\ 2 & 1 & 3 & 1 \\ 0 & 0 & 1 & 2 \end{array}\right]} \end{array} \] And \( \alpha=-0.382 \) and \( \beta=-0.382 \) and the transformation matrix \( [P] \) is given as below; \[ [\boldsymbol{P}]=\left[\begin{array}{llll} 1 & 0 & \alpha & 0 \\ 0 & 1 & 0 & 0 \\ \beta & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right] \] So, find a) \( [P]^{\top}[K][P] \) b) \( [P]^{T}[M][P] \)