## Question

# 1. Let T be the following transformation R2 R2: projecting onto the x, then projecting onto the line y 2x. = line y a)

## 1. Let T be the following transformation R2 R2: projecting onto the x, then projecting onto the line y 2x. = line y a) What is the matrix A for T, using standard basis? b) What are the eigenvalues and eigenspaces of T, using algebraic method and the ma- trix A? c) Explain part b) using geometry. = Problem 2. Let A be the matrix in Problem 1. Find A2023 by: a) Using geometry, using the description of T, and results from Problem 1. b) Using algebra, via diagonalization.

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