Symmetric Matrices: Null Space and Column Space

This lecture explores the properties of symmetric matrices, focusing on proving that the only solution in the kernel of a symmetric matrix is the zero vector. The instructor demonstrates the process step by step, using the symmetry condition to derive a contradiction and establish the uniqueness of the zero vector as the solution. By defining the column space and utilizing the properties of symmetric matrices, the lecture showcases how to reason through the problem and arrive at the desired conclusion.