MAT 262 Lecture 1: Lecture 1 Notes

Let E = {e1, e2, e3, e4} be the standard basis for R4 and let T1,T2,T3,T4 be linear transformations from R4 to R4, about which we are given the following information: T1(e1)=0 T2(e1)=e1 T3(e1)=e1 T4(e1)=e1 T1(e2)=e2 T2(e2)=0 T3(e2)=e2 T4(e2)=e2 T1(e3)=e3 T2(e3)=e3 T3(e3)=0 T4(e3)=e3 T1(e4)=e4 T2(e4)=e4 T3(e4)=e4 T4(e4)=0 Find [T1]EE, [T2]EE, [T3]EE, [T4]EE, and compute the product [T4]EE[T3]EE[T2]EE[T1]EE Hint: There are two solutions: one long and one clever.

f(x, y, z) dzdzdy in the following order: Re-iterate the integral f(x, y, 2) dzdydz where: E to EE to EE to

Evaluate the iterated integral EE Lir.sinundyded /0 Jo Jo