Determine if the following set of polynomials fors a basis of P_3 , p_1=3+7t, p_2=5+t-2t^3 ,p_3=t-2t^2, p_4=1+16t-6t^2+2t^3

generals336 2021-09-13 Answered

Determine if the following set of polynomials fors a basis of P3
p1=3+7t,

p2=5+t2t3,

p3=t2t2,

p4=1+16t6t2+2t3

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Expert Answer

lamanocornudaW
Answered 2021-09-14 Author has 85 answers

We have given the polynomials
p1=3+7t,

p2=5+t2t3,

p3=t2t2,

p4=1+16t6t2+2t3
The coordinate mapping gives the following coordinate vectors
[3700],[5102],[0120] and [11662]
Write the above vectors as a column matrix and reduce the matrix into reduced row echelon form as follows.
[35017111600260202][35011911400130101]
[35011911400130101][19114350100130101]
[19114350100130101][1002350100130101]
[1002350100130101][1002050500130101]
[1002050500130101][1002010100130101]
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