摘要：
The column space of a matrix A tells us when the equation Ax = b will have a solution x. The null space of A tells us which values of x solve the equation Ax = 0. 阅读全文
摘要：
To account for row exchanges in Gaussian elimination, we include a permutation matrix P in the factorization PA = LU. Then we learn about vector spaces and subspaces; these are central to linear algebra. 阅读全文