Linear Algebra lecture1 note

Professor: Gilbert Strang

Text: Introduction to Linear Algebra

http://web.mit.edu/18.06

 

Lecture 1 contents:

n linear equation, n unknowns

Row picture

& Column picture

Matrix form

 


 

引入方程组

image

可表示为AX=b的形式,为:

image

从几何意义上理解,每个方程表示一条直线,两条直线相交于一点,即为方程组的解。以列的形式可以写为:

image

linear combination of columns

观察,很容易得出x=1,y=2

可作向量图加深理解

可表示为AX=b的形式:

image

也可表示为combination of columns:

image

容易观察出x=0,y=0,z=1

思考:Can I solve Ax=b for every b?

Do the linear combinations of column fill 3-D space?

回答:For this A , the answer is yes,

but if 3 vectors in one plane, b unreachable,  singular case(奇异), not invertible(非可逆)

 


 

AX=b   矩阵*向量形式(如何计算): Ax is combinations of columns of A

posted @ 2016-10-26 22:43  nanocare  阅读(107)  评论(0编辑  收藏  举报