Mark each statement as true or false Explain your reasoning

Mark each statement as true or false. Explain your reasoning. Suppose that p_1, p_2, p_3, p_4 and p_5 are all polynomials of degree 3 or less. True or False: The set {p_1, p_2, p_3, p_4, p_5} cannot be linearly independent.

Solution

A set is called a linear independent set if no element in the set can be written as a linear combination of the other elements.

In this question, if we take {p1=x^3,p2=x^2,p3=x,p4=1} now any polynomial p5 can be written as a linear combination of these 4 elements.

Thus the statement is false.