Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Let $P_0(t) = 1, P_1(t) = t, P_2(t) = t^2, P_3(t) = t^3$, then $\{P_0, P_1, P_2, P_3\}$ is linearly independent. Reason R : $C_0 P_0 + C_1 P_1 + C_2 P_2 + C_3 P_3 = 0 \implies C_0 = 0, C_1 = 0, C_2 = 0, C_3 = 0$.
In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Standard monomial sets $\{1, t, t^2, \dots, t^n\}$ are always linearly independent in any polynomial space $\mathcal{P}_n(\mathbb{R})$.

Answer 1

The Correct Option is A