PLEASE FULLY SOLVE AND MAKE ANSWER CLEAR TO READ!!!! **Linear Transformations**A linear transformation is a mathematical function that maps vectors from one vector space to another while preserving the operations of vector addition and scalar multiplication. The transformation T: ℝ² → ℝ² defines a mapping from a two-dimensional vector space to another two-dimensional vector space. **Problem Statement:**Let T: ℝ² → ℝ² be a linear transformation such that T(x₁, x₂) = (x₁ + x₂, 6x₁ + 2x₂). Find x such that T(x) = (1, 22).**Solution Approach:**1. You start with the given transformation: \[ T(x_1, x_2) = (x_1 + x_2, 6x_1 + 2x_2) \] 2. We need to find a vector \( x = (x_1, x_2) \) such that \[ T(x) = (1, 22) \] 3. This gives us two equations to solve: - \( x_1 + x_2 = 1 \) - \( 6x_1 + 2x_2 = 22 \)4. Solve these equations simultaneously to find \( x_1 \) and \( x_2 \).Therefore, you need to solve the system of linear equations to find the vector \( x \) in ℝ² that satisfies the condition given by the transformation T.**Graphical or Diagrammatic Explanation:**- There is no diagram or graph provided in this problem.- This problem focuses on solving the set of linear equations derived from the given transformation.**Input Box:**- There is an input box represented by \( x = \boxed{\phantom{x}} \) where you will enter the solution vector \( x \).Make sure to follow the conditions set by the linear transformation and solve the system of linear equations accurately.

Answered: Let T: R² →R² be a linear…

Let T: R² →R² be a linear transformation such that T (×₁,×₂) = (X₁ + X₂, 6x₁ + 2x₂). Find x such that T(x) = (1,22). X=

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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