Objectives of Matrices
Part 1 | Rank of a Matrix
Part 2 | Consistent and Non-consistent Matrices
Part 3 | Eigen Values and Eigen Vectors
Matrices | Part 1 | Rank of a Matrix
You should be able to know how to determine Rank of a Matrix. This is the most basic step, which will then take you to other complex topics of Matrices. From GATE Point of view, this is the most important Chapter. I have covered only those concepts that are prscribed by S.R.T.M.U Nanded, Maharashtra. The most important concepts, type of questions asked, and other necessary details about the University Exam are provided at the end by expert teachers of MGM's College of Engineering, Nanded. Hope you find the content useful and socialize it by sharing it with your friends! Happy Calculating!
Rank of a Matrix Using Row Transformation
This format of calculating Rank of a matrix is also called the "Cannonical Form".
A matrix is in row echelon form (ref) when it satisfies the following conditions.
The first non-zero element in each row, called the leading entry, 1.
Each leading entry is in a column to the right of the leading entry in the previous row.
Rows with all zero elements, if any, are below rows having a non-zero element.
Note: Some references present a slightly different description of the row echelon form. They do not require that the first non-zero entry in each row is equal to 1.
A matrix is in row echelon form (ref) when it satisfies the following conditions.
The first non-zero element in each row, called the leading entry, 1.
Each leading entry is in a column to the right of the leading entry in the previous row.
Rows with all zero elements, if any, are below rows having a non-zero element.
Note: Some references present a slightly different description of the row echelon form. They do not require that the first non-zero entry in each row is equal to 1.
