Determine whether each set {p1,p2} is a linearly independent set in P^3.The polynomials p_1(t)=1+t^2 and p_2(t)=1−t^2

Trent Carpenter

Trent Carpenter

Answered question

2021-09-09

Determine whether each set {p1,p2} is a linearly independent set in P3.
The polynomials p1(t)=1+t2 and p2(t)=1t2.

Answer & Explanation

Luvottoq

Luvottoq

Skilled2021-09-10Added 95 answers

Given
The polynomial
pt=1+t2 and p2(t)=1t2
Thus scalar multiple of each other
1+t2=a(1t2)
1+t2=aat2
Compare the coefficient,
a=1,a=1
both values cannot be true at the same time. so vector cannot be written as scalar multiple, set is linearly independent

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