4.4 Exercises In Exercises 1-4, find the vector x determined by the given coor- dinate vector [ x ], and the given basis B. 10. B - - [-37 1 . B = In Exercises 11 and 12, use an inverse matrix to find [ x ], for the given x and B. 2. B = $] .[9] . (x 16 - [-$] 11. B = 3. B = 12. B = ([3] . * = [3] 13. The set B = (1 + 12, 1 + (2, 1 + 21 + 12) is a basis for P2. Find the coordinate vector of p(1 ) = 1 + 4t + 712 relative 4. to B. 14. The set B = {1 - 12, 1 - 12,2 - 21 + 12; is a basis for P2. In Exercises 5-8, find the coordinate vector [ x ], of x relative to Find the coordinate vector of p() = 3 + 1 -612 relative the given basis B = {b, ..., b,, }. to B. 5. bi = _3 . ">2 - [ 3]. x - [ ] In Exercises 15-20, mark each statement True or False (T/F). Justify each answer. Unless stated otherwise, 1 is a basis for a vector space V. 6. DI = 2 .12 - [8].x= 6 15. (T/F) If x is in V and if 3 contains n vectors, then the B- coordinate vector of x is in IR" 7. by = -1 . b. - . " - [-3].~ - [-5] 16. (T/F) If B is the standard basis for R", then the 3-coordinate vector of an x in R" is x itself. 17. (T/F) If PB is the change-of-coordinates matrix, then [x]s = PB X, for x in V. 18. (T/F) The correspondence [ X ] > x is called the coordinate