Recently,in order to get ready for postgraduate stage study ,my tutor give me a MIT website to review linear algebra ,I record important information.
Today,I learned L3 which is about inverse matrix. The professor give evidence that which matrixes are singular:
first,determinant equals to zero.Because the lines represented by the rows in the matrix are all parallel,so when this matrix times every other matxix which is not zeros,the result will be parallel,too.
second,if exits a matrix X which is not a zero and AX=0,then matrix A is singular, non-invertible.Because suppose exist a A' and A'A=I,then A'AX=IX=X,but A'0=0.so we can include :X=0 which is opposite to that :X is not a zero.
中文理解：事实上本节就是讲述一个事实：行列式为0的矩阵不可逆，如果存在一个非0矩阵X，使得矩阵AX=0的话，则A矩阵不可逆。
简单理解：1，若行列式为0，则矩阵中每一行代表的直线都是同一方向的（非（0,1）），那无论与哪个矩阵点乘结果都在同一条直线上，都不会成为单位阵中的每一行所指示的方向。关于第二个可以理解为：如果矩阵A中所代表的每一条直线可以通过非0的线性组合得到原点（（0,0）），则说明每条直线都一定是同向的，因为如不同向，则通过非0的现象组合，两向量的和一定不会为0，只要证明了两条直线同向，接下来的证明就同1.
完