Let V be the subspace of R2x2 spanned by the matrices where b ^ 0.a. Compute P2 and find the coordinate vector [^2]s^ where 3^ = (I2, P) . b. Consider the linear transformation T(M) = M P from V to V. Find the 23-matrix B of T. For which matrices P is T an isomorphism? c. If T fails to be an isomorphism, find the image and kernel of T. What is the rank of T in that case?

Lecture 7: Limits (Section 2.2) Recall the deﬁnition: For a given function f(x), we say that x→c f(x)= L if we can make the values of f(x)aseto L as we want by choosing x suﬃciently close to c on either side but not equal to c. ▯ ex. If f(x)= x if x ▯=1 ,dml f(x). f3i x =1 x→1 ▯ ex. If g(x)= f 3i x ≤ 0 ,ndl g(x). −f1i x> 0 x→0