Ax = 0, the Homogenous Solution

In this video I talk about the linear algebra topic Ax = 0, also known as the Homogenous Solution. This is a concept of solving systems of linear equations. The idea of a homogeneous solution is important in linear algebra because it allows us to classify systems of linear equations based on the number and type of solutions they have. For example, a system of linear equations that has no solutions is called inconsistent, while a system of linear equations that has a unique solution is called consistent and independent. A system of linear equations that has infinitely many solutions is called consistent and dependent. In summary, the concept of a homogeneous solution is important in linear algebra because it allows us to classify systems of linear equations based on the number and type of solutions they have. It is also closely related to other important concepts in linear algebra, such as the null space of a matrix and the rank-nullity theorem.
#Ax=0 #homogenoussolution #solveamatrix

[jayavionharris]

Yo bro you saved my life with this. I've been just goin through the motions of set theory and realized that I never fully understood homogenous solutions and (non)trivial solutions. Saved me about an hour of note compiling and conclusions, so thanks for this!

[greatsea]

in wolfram and ti-84 reducing (rref) gives [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], not what you got. Obv. I could be missing something, just thought I'd mention.