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(Solved): If B is the standard basis of the space P_(3) of polynomials, then let B={1,tt^(2),t^(3)}. Use coor ...
If
Bis the standard basis of the space
P_(3)of polynomials, then let
B={1,tt^(2),t^(3)}. Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work.
1-7t^(2)-t^(3),t+6t^(3),1+t-7t^(2)Write the coordinate vector for the polynomial
1-7t^(2)-t^(3).
(1,0,-7,-1)Write the coordinate vector for the polynomial
t+6t^(3).
(0,1,0,6)Write the coordinate vector for the polynomial
1+t-7t^(2).
(1,1,-7,0)To test the linear independence of the set of polynomials, row reduce the matrix which is formed by making each coordinate vector a column of the matrix. If possible, write the matrix in reduced echelon form.
[[1,0,1],[0,1,1],[-7,0,-7],[-1,6,0]]∼