Linear Algebra: Linear Transformations and Matrices

This lecture covers the concept of linear transformations, where any machine that respects vector addition and scalar multiplication is considered. It explores the relationship between linear transformations and matrices, emphasizing the importance of bases in determining the matrix associated with a linear transformation. The lecture delves into finding the kernel and image of a linear transformation, showcasing examples with polynomials and matrices. It also discusses the dimension of the kernel and image, illustrating how to characterize them using the null space and column space of a matrix. The lecture concludes with a practical application of determining the kernel and image of a specific linear transformation.