1.1.48 Vector Algebra
condition: Given vectors: \( \bar{a}_{1}=(-1,0,3), \bar{a}_{2}=(2,2,1) \), \( \bar{a}_{3}=(-7,-6,0), \bar{a}_{4}=(5,-4,1) \). a) Find the rank and basis of the set of vectors \( M=\left\{\bar{a}_{1}, \bar{a}_{2}, \bar{a}_{3}, \bar{a}_{4}\right\} \) and express all vectors of the set \( M \) in terms of basis vectors. b) Find all vectors orthogonal to the vector \( \bar{a}=(-1,3,2) \).
Vector algebra is a branch of algebra that studies linear operations on vectors and their geometric properties. In the section you will find problems on the decomposition of vectors, scalar, vector and mixed products, coordinates of vectors in different bases and much more.