Geometric View on Solutions to Ax=b and Ax=0.

Learning Objectives:
1) Algebraically solve systems like Ax=b and Ax=0
2) View the solutions geometrically
3) Compare how solutions to Ax=b are parallel to solutions for Ax=0, the latter of which goes through the origin

This video is part of a Linear Algebra course taught at the University of Cincinnati.

[TomerBenDavid]

25 years later since studying this at CS which was a nightmare now with this lecturer I enjoy it so much!

[まつまつ-xf]

The geometric graph greatly helps me to understand why a linear transformation with horizontal and vertical moving fails to be a transformation since they do not pass the origin.

[kamalmakhloufi]

Thank you so much for this lesson .your explanation is really clear .

[pacchutubu]

Thanks for the insight. My question is, since they are just parallel lines (here), why are the equations categorized as homogeneous and non-homogeneous?

[patrikengas]

1:26, why is it written x3=s in the homogeneous system? isn't it in 2 variables?

[JoaoVitorBRgomes]

Why in the homogenous system the vector is ( 2 -1) shouldn't it be (2 0) since x1 = -2*S + 0 ?

[kylebossify]

Would anybody know of any practice problems that could go along with these videos that you would reccomend?

[wakeawake]

Sir, plz suggest me a book to learn linear algebra plzzz🙏🙏🙏