e have stated that [1; x; x^2; ......; x^n] is a basis for Wn, where Wn denotes the vector space of polynomials of maximal degree n. Verify that [1; x -1; x^2 - x; : : : ; x^n -x^n-1] is also a basis for Wn
Now for this i was generally thinking of subbing in values for the relevant x's but is this correct? Q3)Let V be a vector space with basis [v1; v2; v3]. Which of the following collections are also a basis for V ? 1) [v1, v1 + v2, v1 + v3] 2) [2v1,3v2, v1 + v2]; 3) [v1, v2 + v3, v1 -v3, v1 + v2] 4) [v2, v3 - v, v3 + v2] 5) [ v2, v3- v1] 6) [v1 - v2 + 2v3 , 2v2 + v3, 3v1 + v2 -3v3]
Again is it easier to just make values for v1,v2,v3 up ?