Determine whether each set {p1,p2} is a linearly independent set in P3. 1. The polynomials p1 (t) = 1 + t2 and p2(t) = 1 - t2.
2. The polynomials p1 (t) = 2t + t2 and p2(t) = 1 + t.
3. The polynomials p1(t) = 2t - 4t2 and p2(t) = 6t2 - 3t.

1) The polynomials and are linearly independient, 2) The polynomials and are linearly independent, 3) The polynomials and are linearly dependent.

Step-by-step explanation:

A set is linearly independent if and only if the sum of elements satisfy the following conditions:

1) The set of elements form the following sum:

From definition this system of equations must be satisfied:

Eq. 1

Eq. 2

From Eq. 2:

In Eq. 1:

The polynomials and are linearly independient.

2) The set of elements form the following sum:

From definition this system of equations must be satisfied:

The polynomials and are linearly independent.

3) The set of elements form the following sum:

From definition this system of equations must be satisfied:

(Eq. 1)

(Eq. 2)

It is easy to find that each coefficient is multiple of the other one, that is:

(From Eq. 1)

(From Eq. 2)

Which means that polynomials and are linearly dependent.

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step-by-step explanation: