Introduction to Linear Algebra and Its Applications Exam Questions and answers

Introduction to Linear Algebra and Its Applications Exam Questions and answers What is Linear Algebra primarily concerned with? - Solving equations, particularly simultaneous linear equations, and building a theoretical framework to enhance their application. What are the basic operations you should know with column vectors? - Adding vectors (v + w) and multiplying them by scalars (λv) where v, w ∈ R^n and λ ∈ R. How do you multiply a column vector by a matrix? - By multiplying a column vector v ∈ R^n by an m × n matrix A to obtain a new column vector Av ∈ R^m. What is the dot product of two column vectors used for? - To compute the length of a vector, the angle between two vectors, or to project one vector onto another.