In control engineering and structural dynamics, mathematical models such as the state-space representation, equation-of-motion, and the phase plane are matrix equations describing the system equilibrium. This paper develops novel matrix equations models for linear/nonlinear dynamic analysis of reinforced concrete (RC) buildings with cantilever elements lateral load resisting system (e.g., RC shear wall, RC core). The matrix equations models offer a reliable and idealized tool for introducing two-dimensional and three-dimensional cantilever structures to control engineering and structural dynamics' equation-of-motion. The displacement-related stiffness matrix of cantilever elements is determined using the Left Riemann Sums (LRS) numerical integration method that yields transformation matrices that cater to the element's boundary conditions. The three-dimensional structure's mass and stiffness matrices are determined using the Direct Stiffness Method (DSM) and local-to-global-coordinates transformation matrices. The nonlinear matrix structural analysis employs a smooth hysteretic model for deteriorating inelastic structures, referring to the relation between the bending moment and the bending-curvature through the bending-stiffness. The parameters controlling the cyclic behavior regard a composite RC cross-section subject to gravitational load and bending simultaneously. The paper includes four examples that exemplify the practical utilization of the matrix equations models in analyzing two-dimensional and three-dimensional structures of linearly-elastic and inelastic properties. The four examples demonstrated the idealized applicability of the matrix equations models that suit state-space, equation-of-motion, and phase plane analyses.