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Vector Spaces Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

	Mathematics for IIT JAM, GATE, CSIR NET, UGC NET 556 videos\|198 docs

Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

556 videos|198 docs

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FAQs on Vector Spaces Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

1. What is a vector space?

Ans. A vector space is a mathematical structure that consists of a set of vectors and two operations: vector addition and scalar multiplication. It satisfies certain properties, such as closure under addition and scalar multiplication, and the existence of an additive identity and additive inverses.

2. What are the properties of a vector space?

Ans. A vector space must satisfy several properties, including closure under vector addition and scalar multiplication, associativity and commutativity of vector addition, existence of an additive identity and additive inverses, distributivity of scalar multiplication over vector addition, and compatibility of scalar multiplication with field multiplication.

3. Can a set of matrices form a vector space?

Ans. Yes, a set of matrices can form a vector space if it satisfies the properties of a vector space. Matrices can be added together and multiplied by scalars, and these operations satisfy the required properties. For example, the set of all 2x2 matrices with real number entries is a vector space.

4. What is a subspace in a vector space?

Ans. A subspace is a subset of a vector space that also forms a vector space itself. It must satisfy the properties of closure under vector addition and scalar multiplication, and contain the additive identity and additive inverses. For example, the set of all polynomials of degree 2 or less is a subspace of the vector space of all polynomials.

5. What is the dimension of a vector space?

Ans. The dimension of a vector space is the number of vectors in a basis for that vector space. A basis is a set of linearly independent vectors that spans the entire vector space. The dimension of a vector space can be thought of as the "size" or "degree of freedom" of the space. For example, the dimension of the vector space of all 3-dimensional vectors is 3.

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Mathematics IIT JAM

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Mar 07, 2025 Last updated

Video Description: Vector Spaces for Mathematics 2025 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation. The notes and questions for Vector Spaces have been prepared according to the Mathematics exam syllabus. Information about Vector Spaces covers all important topics for Mathematics 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Vector Spaces.

Introduction of Vector Spaces in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Vector Spaces in Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET course. Download more important topics related with notes, lectures and mock test series for Mathematics Exam by signing up for free.

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Video Lecture & Questions for Vector Spaces Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.

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Here you can find the meaning of Vector Spaces defined & explained in the simplest way possible. Besides explaining types of Vector Spaces theory, EduRev gives you an ample number of questions to practice Vector Spaces tests, examples and also practice Mathematics tests.

	Mathematics for IIT JAM, GATE, CSIR NET, UGC NET 556 videos\|198 docs

Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

556 videos|198 docs

Join Course for Free

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