Question: Math 2641 (Fall 2022) Homework Set #04 (Due 09/23) Problems Problem 4.1. Define T: R2 - R3 by T(x) = 21 - 202 for all

Math 2641 (Fall 2022) Homework Set #04 (Due 09/23) Problems Problem 4.1. Define T: R2 - R3 by T(x) = 21 - 202 for all x = 2.X1 - 22 [:2] . Let b = 4 (1) Find the standard matrix A for the linear transformation T. (2) Determine whether there exists x E R2 such that T(x) = b. Problem 4.2. Consider the following matrices A = -2 7 0' B = O Compute the following: (1) AT; (2) BT; (3) A - 2BT. Problem 4.3. Consider the following matrices 4- [2 7 8. B- O Compute the following: (1) AB; (2) BC; (3) C2 Problem 4.4. Find the inverse of the following matrix A, or otherwise state that its inverse does not exist. A = ON
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