Linear Algebra – Post 2 – Linear combination & Span , Linear Dependence & Linear Independence

Linear Algebra

Linear Combination and Span: Given a set of vectors, what other vectors can you create by adding and/or subtracting scalar multiples of those vectors. The set of vectors that you can create through these linear combinations of the original set is called the “span” of the set. More generally, a linear combination of n vectors v1, v2, . . . , vn is any vector of the form a1v1 + a2v2 + · · · + anvn where a1, a2, . . . , an are scalars The set of…

Linear Algebra Series – Post – 1- [Vectors & Scalars]

Linear Algebra

Vectors & Scalars: The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar Vector is a representation of both magnitude and direction. Scalar , represents only the magnitude or the numeric value. For Example: The forces which operate on a flying aircraft, the weight, thrust, and aerodynmaic forces, are all vector quantities. The resulting motion of the aircraft in terms of displacement, velocity, and acceleration are also vector quantities. These quantities can be…