Please solve only question a. ### Linear Algebra Problem on Linear Transformation**Problem 2:**Linear transformation $ L $ is given by the formula below. Find the matrix of $ L $, the domain, the co-domain, the kernel, and the range using methods of linear algebra. Make sure to show all work and clearly mark the answers.#### Question a.\[ L(x, y) = \langle x - y, x + y, -x + y, y \rangle \]#### Question b.\[ L(x, y, z, w) = \langle x + y + z + w, x - w \rangle \]For each question, you will need to:1. **Find the Matrix Representation of $ L $:** Write the transformation in matrix form.2. **Determine the Domain:** Identify the vector space from which the inputs to the transformation $ L $ are from.3. **Determine the Co-domain:** Identify the vector space where the outputs of the transformation $ L $ land.4. **Calculate the Kernel (Null Space):** Find all input vectors that map to the zero vector under $ L $.5. **Calculate the Range (Column Space):** Determine the set of all possible output vectors of the transformation $ L $.Make sure you label and organize your steps clearly to ensure complete understanding of how each property of the linear transformation is determined.

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Description: Please solve only question a. ### Linear Algebra Problem on Linear Transformation**Problem 2:**Linear transformation $ L $ is given by the formula below. Find the matrix of $ L $, the domain, the co-domain, the kernel, and the range using methods

Given, Linear transformation is given by,

Answered: Linear transformation L

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Linear transformation L

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 18RE

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Please solve only question a.

### Linear Algebra Problem on Linear Transformation

**Problem 2:**
Linear transformation $ L $ is given by the formula below. Find the matrix of $ L $, the domain, the co-domain, the kernel, and the range using methods of linear algebra. Make sure to show all work and clearly mark the answers.

#### Question a.
\[ L(x, y) = \langle x - y, x + y, -x + y, y \rangle \]

#### Question b.
\[ L(x, y, z, w) = \langle x + y + z + w, x - w \rangle \]

For each question, you will need to:

1. **Find the Matrix Representation of $ L $:** Write the transformation in matrix form.
2. **Determine the Domain:** Identify the vector space from which the inputs to the transformation $ L $ are from.
3. **Determine the Co-domain:** Identify the vector space where the outputs of the transformation $ L $ land.
4. **Calculate the Kernel (Null Space):** Find all input vectors that map to the zero vector under $ L $.
5. **Calculate the Range (Column Space):** Determine the set of all possible output vectors of the transformation $ L $.

Make sure you label and organize your steps clearly to ensure complete understanding of how each property of the linear transformation is determined.

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