1.1.50 Vector Algebra
Condition: a) Indicate two different bases of the space \( \mathbb{R}^{4} \). b) Find the orthonormal basis of the subspace of solutions to a homogeneous system of linear equations \( \left\{\begin{array}{c}x_{1}+3 x_{2}-x_{3}=0 \\ -2 x_{1}-6 x_{2}+2 x_{3}=0\end{array}\right. \)
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.