33. Let T: P₂→ P₂ be defined by T(ax² + bx + c) = ax^2 + (a-2b)x + b a. Determine whether p(x) = 2x^2 - 4x +6 is in the range of T. b. Find a basis for R(T).
Question
Solution 1
a. To determine whether p(x) = 2x^2 - 4x + 6 is in the range of T, we need to find some polynomial q(x) = dx^2 + ex + f such that T(q(x)) = p(x).
T(q(x)) = T(dx^2 + ex + f) = dx^2 + (d-2e)x + e
Setting this equal to p(x), we get:
dx^2 + (d-2e)x + e = 2x^2 - 4x + 6
Comparing coefficients, we get Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
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