3. Later in the course we will demonstrate that the following column vector {N}: N N...

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3. Later in the course we will demonstrate that the following column vector {N}: N N N3 = = = 1 1 (2x (xL - - 3xL + 1) 2xL + x) (-2x + 3x1) N = (x - x) L Are the shape functions for a Bernoulli-Euler beam element. For a beam the nodal displacements include the two translations vi and v as well as the two rotations 0 and 02. These displacements form the vector {d}. c) Are the polynomial shape functions above linearly independent? d) Are the polynomial shape functions above orthogonal? 3. Later in the course we will demonstrate that the following column vector {N}: N N N3 = = = 1 1 (2x (xL - - 3xL + 1) 2xL + x) (-2x + 3x1) N = (x - x) L Are the shape functions for a Bernoulli-Euler beam element. For a beam the nodal displacements include the two translations vi and v as well as the two rotations 0 and 02. These displacements form the vector {d}. c) Are the polynomial shape functions above linearly independent? d) Are the polynomial shape functions above orthogonal?