- #1
Muthumanimaran
- 81
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What does a rank of a matrix mean? why it is important? what does it tells you about?
The matrix rank is the maximum number of linearly independent rows or columns in a matrix. In other words, it is the number of non-redundant equations or variables in a system of linear equations represented by the matrix.
The matrix rank is an important concept in linear algebra as it provides information about the dimensionality of a matrix and the solutions to systems of linear equations. It can also be used to determine whether a matrix is invertible, which is a crucial property in many applications.
A high matrix rank indicates that the matrix is full rank, meaning all of its rows and columns are linearly independent. This means that the matrix has a unique solution to a system of linear equations and is therefore invertible.
The matrix rank can be calculated by performing elementary row or column operations on the matrix until it is in reduced row-echelon form. The number of non-zero rows or columns in the reduced form is then the matrix rank.
Yes, a matrix can have a rank of zero if all of its rows and columns are linearly dependent. This means that the matrix has no unique solution to a system of linear equations and is therefore not invertible.