Rank of Matrices (Engineering Maths 1)

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In this video you will learn the following Concept :

The rank of a matrix is a fundamental concept in linear algebra that measures the dimension of the vector space spanned by its rows or columns. Specifically, it represents the maximum number of linearly independent rows or columns in the matrix.

Key points include:

1. Definition: The rank can be found by determining the number of leading ones in the row echelon form or reduced row echelon form of the matrix.
2. Properties:
   • The rank is always less than or equal to the smaller of the number of rows or columns.
   • A full rank matrix has a rank equal to the lesser of its dimensions.
   • The rank of a matrix can also indicate the number of solutions to a system of linear equations it represents.
3. Applications: Rank is used in various fields, including statistics, computer science, and engineering, to analyze systems of equations, understand data structures, and perform dimensionality reduction.

Understanding the rank helps in evaluating the solvability of linear systems, the effectiveness of transformations, and the overall structure of data.

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