Problem of the week - Is the spanning set a basis?
December 12, 2018
Vector spaces are one of the key subjects of linear algebra, and their theory has found application in mathematics, engineering, physics, chemistry, biology, the social sciences, and other areas. The theory, basically, consists in generalizing the familiar ideas of geometrical vectors of calculus to vectors of any size, but it provides an abstract, coordinate-free way of dealing with geometrical and physical objects such as tensors. The beauty of vector spaces theory can be found in every problem, where many of them, are just the appropriate linear-algebraic notion of very well known problems like solving systems of linear equations.
The problem of this week is related to spanning sets and bases, two key concepts from vector spaces you should master. The solution, as usual in most of Linear Algebra problems, uses basic concepts from matrices and their operations.
