1.7.20 Linear Transformations

Condition: Vectors \ (\ Overline {A_ {1}, \ Overline {A_ {2}, \ LDOTS \) and vector \ (\ bar {x} \) are set by their coordinates in the standard basis. Find the coordinates of the vector \ (\ bar {x} \) in the basis \ (\ overLine {a_ {1}}, \ overLine {a_ {2}, \ ldots \), as well as in the basis \ (\ overLine {b_ {1}}, \ overLine {b_ {2}}, \ ldots \) if \ [\ begin {array} {l} \ text {a) \ bar {x} = (12.6, -10); \ Overline {a_ {1}} = (-2, -1,4), \ overLine {A_ {2} = (0-3.0), \\ \ ERLINE {3}} = (4, -1, -1), \ Overline {B_ {1}} = 4 \ overline {a_ {1}}+3 \ overLine {a_ {2}}-3 \ overLine {a_ {3}}, \\ \ overline {b_ {2}} =-3 \ overLine {a_ {1}}-2 \ overline {a_ {2}}-1 \ overLine {a_ {3}}, \ overLine {b_ {3} =-3 \ overlin