1.1.42 Vector Algebra

Condition: set the vector \ (a \) and the system of vectors \ (v \). 1) Find the rank of vectors system: \ (r g (v), 2) \) Find the basis of the system in \ (V, 3) \) Find the linear shell \ (\ Mathcal {l} (v), 4) \) Find out if that \ (a \ in \ Mathcal {l} (v) \), 5) to expand the vectors of the system \ (v \) (v \) (v \) (v \) according to the 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) \] \]