How to Find rank using determinant and row echelon form is explained.
What is Rank of a Matrix :
Rank of a matrix is defined as the maximum number of linearly independent Rows/Columns in the Matrix .or
The rank is how many of the rows are "unique": not made of other rows. or
Number of non-zero rows in its row echelon matrix.
Determine Rank using Determinant method:
Find the determinant of the given matrix. If determinant of a matrix is not equal to 0 then the rank of a matrix is equal to the order of the matrix i.e
Det(A)≠0 then Rank of a matrix= order of the matrix .
If determinant of a matrix is equal to 0 then the rank of a matrix is not equal to the order of the matrix i.e
Det(A)=0 then Rank of a matrix≠ order of the matrix .
Then find the determinant of a sub matrix and check again if determinant is equal to zero or not.
Rank of a matrix can never be 0 except the rank of zero matrix .
Find Rank by reducing to Row Echelon Form:
To find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.
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