1.1.42 Vector Algebra
condition: The vector \( a \) and the system of vectors \( v \) are given. 1) Find the rank of the system of vectors: \( r g(v), 2) \) find the basis of the system in \( v, 3) \) find the linear span \( \mathcal{L}(v), 4) \) find out whether it is true that \( a \in \mathcal{L}(v) \), 5) expand the vectors of the system \( v \) by basis in \(v\). \[ a=(1 ; 1 ; 1), \quad v=\left(\begin{array}{c} (0 ; 2 ; 1) \\ (1 ; 2 ; 0) \\ (1 ; 0 ;-1) \\ (1 ; 4 ; 1) \end{array}\right) \]
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.