Find the kernel and range of each of the following linear operators on P^3 (the vector space of polynomials with degree less than 3): (a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c. (b) L(p(x)) = p(x) − p′(x).
Find the kernel and range of each of the following linear operators on P^3 (the vector space of polynomials with degree less than 3): (a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c. (b) L(p(x)) = p(x) − p′(x).
Find the kernel and range of each of the following linear operators on P^3 (the vector space of polynomials with degree less than 3): (a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c. (b) L(p(x)) = p(x) − p′(x).
Find the kernel and range of each of the following linear operators on P^3 (the vector space of polynomials with degree less than 3): (a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c.
(b) L(p(x)) = p(x) − p′(x).
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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