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Concept of Linear Transformation Video Lecture | Mathematics for Competitive Exams
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FAQs on Concept of Linear Transformation Video Lecture - Mathematics for Competitive Exams
| 1. What is a linear transformation in mathematics? |  |
Ans. A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. It maps vectors from one space to another in a way that maintains the linearity of the original vector space.
| 2. How is linearity defined for a linear transformation? | |
Ans. Linearity for a linear transformation is defined by two properties: preservation of vector addition and preservation of scalar multiplication. This means that for any two vectors u and v in the domain of the transformation and any scalar c, the transformation of the sum of u and v is equal to the sum of the individual transformations of u and v, and the transformation of the scalar multiple of u is equal to the scalar multiple of the transformation of u.
| 3. What are some examples of linear transformations? | |
Ans. Some examples of linear transformations include rotation, scaling, reflection, projection, and shearing. These transformations preserve the linearity of vector spaces by preserving vector addition and scalar multiplication.
| 4. How can linear transformations be represented mathematically? | |
Ans. Linear transformations can be represented mathematically using matrices. Each linear transformation has a corresponding matrix representation, and the transformation of a vector can be obtained by multiplying the matrix representation of the transformation with the vector.
| 5. What are the applications of linear transformations in real life? | |
Ans. Linear transformations have various applications in real life, such as in computer graphics, image processing, data analysis, and engineering. They are used to transform and manipulate data, images, and signals in a linear and predictable manner, allowing for efficient and accurate computations and analyses.
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Dec 23, 2024 Last updated |
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