1. Let T: R² → R2 be the linear transformation T[*]-[***] a) Find [T] where a is the standard basis for R². b) Let 6 be the basis consisting of X2 x2 -2 [3][7] for R2. Find the change of basis matrix from a to ß. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for v=[²3] · f) Find [T(v)]. g) Use the result of part (f) to find T (v).

You work at a company called 'PulseTech'. The startup is about to launch a new smart wristband that has a photoplethysmogram (PPG) sensor that monitors heart rhythms. This sensor captures a reading every 60 seconds, represented by beats per minute (bpm). Imagine you possess this heart rate information for N individuals, gathered over a span of one day, and you save it in a vector hi for i = 1, 2, 3, ..., N.

Draw two vectors, v and w, with the same initial point. Show the vector projection of v onto w in your diagram. Then describe how you identified this vector.

Show the process of Reflecting a vector/matrix about a line that goes through the origin?