coordinate-x-2-to-basis-x-2-x-x-1-x-2-1-at-P-2-is-

Question Number 54939 by gunawan last updated on 15/Feb/19

coordinate x^{2} to basis {x^{2} + x, x + 1, x^{2} + 1}

at P_{2} is \dots

Commented by Abdo msup. last updated on 15/Feb/19

l e t f i n d α, β a n d γ w i t h v e r i f y

x^{2} = α (x^{2} + x) + β (x + 1) + γ (x^{2} + 1) \forall x \Rightarrow

x^{2} = (α + γ) x^{2} + (α + β) x + β + γ \Rightarrow

{\begin{cases} α + γ = 1 \\ α + β = 0 a n d β + γ = 0 \Rightarrow α - γ = 0 \Rightarrow γ = α \Rightarrow α = \frac{1}{2} \end{cases}

= γ a n d β = - γ = - \frac{1}{2} s o

x^{2} = \frac{1}{2} (x^{2} + x) - \frac{1}{2} (x + 1) + \frac{1}{2} (x^{2} + 1)

s o x^{2} (\frac{1}{2}, - \frac{1}{2}, \frac{1}{2}) i n t h a t b a s i s .

Commented by gunawan last updated on 15/Feb/19

thank y o u very much Sir

Commented by Abdo msup. last updated on 15/Feb/19

y o u a r e w e l c o m e .