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Vector intro for linear algebra Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
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FAQs on Vector intro for linear algebra Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a vector in linear algebra? |  |
Ans. In linear algebra, a vector is a mathematical object that has both magnitude and direction. It can be represented as an ordered list of numbers, called coordinates, or as an arrow in space. Vectors are commonly used to represent physical quantities such as displacement, velocity, and force.
| 2. How are vectors represented in linear algebra? | |
Ans. Vectors in linear algebra can be represented in different ways. One common representation is as a column matrix, where each element in the column represents the magnitude or value of the vector component. Another representation is as a row matrix, where the elements are arranged in a horizontal line. Vectors can also be represented graphically as arrows in space.
| 3. What is the difference between a scalar and a vector in linear algebra? | |
Ans. In linear algebra, a scalar is a single number that represents a magnitude or value, but it does not have a direction. On the other hand, a vector has both magnitude and direction. Scalars can be added, subtracted, multiplied, and divided by scalars or vectors, while vectors can be added or subtracted from each other.
| 4. How are vectors added and subtracted in linear algebra? | |
Ans. In linear algebra, vectors are added or subtracted by adding or subtracting their corresponding components. For example, if two vectors are represented as column matrices, their addition would involve adding the corresponding elements of each column. Similarly, subtraction would involve subtracting the corresponding elements. The result is a new vector with the same dimensionality as the original vectors.
| 5. What are the applications of vectors in linear algebra? | |
Ans. Vectors have various applications in different fields. In physics, vectors are used to represent physical quantities such as velocity, acceleration, and force. They are also used in computer graphics, robotics, and engineering to represent spatial transformations and movements. Vectors are also fundamental in calculus, where they are used to define derivatives and gradients.
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