1.1.31 Vector Algebra
Condition: Given columns \( \quad a=(-1 ;-3 ; 5 ;-3)^{T} \quad \) and \( b=(5 ;-4 ; 5 ;-4)^{T} \). Find a column \( c \in \mathbb{R}^{4} \) orthogonal to \( a \) so that the linear hulls \( \langle a, c\rangle \) and \( \langle a, b\rangle \) coincide.
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.