1.7.10 Linear Transformations

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