Linear Algebra Full Version 线性代数要点摘要 英文版

The essential information of a linear system can be recorded compactly in a rectangular array called a matrix. A matrix containing only the coefficients of a linear system is called the coefficient matrix, while a matrix also including the constant at the end of a linear equation, is called an augmented matrix. The size of a matrix tells how many columns and rows it has. An m × n matrix has m rows and n columns. There are three elementary row operations. Replacement adds to one row a multiple of another. Interchange interchanges two rows. Scaling multiplies all entries in a row by a nonzero constant. Two matrices are row equivalent if there is a sequence of row operations that transforms one matrix into the other. If the augmented matrices of two linear systems are row equivalent, then the two systems have the same solution set.