1.7.10 Linear transformations

Condition: Vectors \( a, b, c, d \) are specified by their coordinates in the canonical basis \( i, j, k \) of the space \( \mathbb{V}_{3} \). 1) Show that the vectors \( a, b, c \) form the basis of the space \( \mathbb{V}_{3} \). 2) Find the coordinates of the vector \(d\) in the basis \(a, b, c\) (using the transition matrix). Do a check. \[ \begin{array}{lll} a=(-3 ; 4 ; 3), & b=(-1 ; 2 ; 3) \\ c=(1 ; 0 ;-1), & d=(1 ; 0 ;-9) \end{array} \]