Let beta = (x^{2} - x, x^{2} + 1,x - 1), beta' = (x^2 - 2x - 3, - 2x^2 + 5x + 5, 2x^2 - x - 3) be ordered bases for P_2(C). Find the change of coordinate matrix Q that changes beta ' -coordinates into beta -coordinates.

Sinead Mcgee 2021-02-08 Answered
Let β=(x2x,x2+1,x1),β=(x22x3,2x2+5x+5,2x2x3) be ordered bases for P2(C). Find the change of coordinate matrix Q that changes β -coordinates into β -coordinates.
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Expert Answer

unessodopunsep
Answered 2021-02-09 Author has 105 answers

LET A = 110122101251011353

It may be observed that the entries in the columns of A are the coefficients of x2, x and the scalar multiples of 1 in the ordered bases β and β’ respectively. To determine the change of coordinates matrix from ββ, we will reduce A to its RREF as under: Add 1 times the 1st row to the 2nd row Add -1 times the 2nd row to the 3rd row Multiply the 3rd row by -1/2 Add -1 times the 3rd row to the 2nd row Add -1 times the 2nd row to the 1st row The RREF of A is 100363010241001112 

Then the change of coordinates matrix from β to β is Q= 363241112

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