If B is the standart basis of the space P_3 of polynomials, then let B=1,t,t^2,t^3. Use coordinate vectors to test the linear independence

mattgondek4

mattgondek4

Answered question

2021-09-14

If B is the standart basis of the space P3 of polynomials, then let B=1,t,t2,t3. Use coordinate vectors to test the linear independence of the set of polynomials below. Explain you work.
1+3t2t3,t+6t3,1+t+3t2

Answer & Explanation

Mitchel Aguirre

Mitchel Aguirre

Skilled2021-09-15Added 94 answers

Given that B={1,t,t2,t3} be the standard basis of the space P3 of polynomials.
and a set of polynomials.
{1+3t2t3,t+6t,1+t+3t2}
We can write
1+3t2t3=1+0.t+3.t2+(1).t3
Therefore
the coordinate vector for the polynomial 1+3t2t3
(1,0,2,-1)
we can write
t+6t3=0+1.t+6.t2+0.t3
Therefore
the coordinate vector for the polynomial t+6t2
(0,1,6,0)
we can write
1+t+3t2=1+1.t+3.t2+0.t3
Therefore
the coordinate vector for the polynomial 1+t+3t2
(1,1,3,0)

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