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Seat No.: ___ Enrolment No.___ GUJARAT TECHNOLOGICAL UNIVERSITY BE SEMESTER 1st / 2ndEXAMINATION (NEW SYLLABUS) WINTER 2018Subject Code: 2110015 Subject Name: Vector Calculus and Linear Algebra Time:10:30
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Understand the basic concepts of linear algebra such as vectors, matrices, and systems of linear equations.
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Learn about vector operations such as addition, scalar multiplication, dot product, and cross product.
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Practice solving linear algebra problems using matrices and determinants.
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Study eigenvalues, eigenvectors, and diagonalization techniques.
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Linear algebra is a branch of mathematics that deals with vectors, vector spaces, linear transformations, and systems of linear equations. A vector is an element of a vector space, typically represented as an ordered array of numbers, which can be used to represent quantities with both magnitude and direction.
Linear algebra and vector do not require filing as they are mathematical concepts. However, if referred to in a context like academic or research submissions, students and professionals in mathematics, engineering, physics, and computer science may need to submit relevant work or findings.
To fill out information related to linear algebra and vector, one typically needs to provide definitions, examples of vector operations (like addition and scalar multiplication), and applications in various fields. If referring to an online platform or academic submission, it would involve entering mathematical expressions and explanations based on specified guidelines.
The purpose of linear algebra and vectors is to provide a framework for analyzing and solving linear problems. They are foundational in various applications such as computer graphics, machine learning, optimization, and robotics, where multi-dimensional data representation and manipulation are essential.
Typically, one must report on concepts like vector definitions, properties (such as length and direction), operations (addition, subtraction, dot product), and application areas. In academic settings, it may also include theorems, proofs, and problem solutions.
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