The formula to calculate the rank of a matrix is:
\[ \text{Rank} = r \]
Where:
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It represents the dimension of the vector space spanned by the rows or columns of the matrix. To calculate the rank of a matrix, perform row operations to reduce the matrix to its row echelon form or reduced row echelon form. The number of non-zero rows in the resulting matrix is the rank of the original matrix.
Let's assume the following matrix:
1, 2, 3 4, 5, 6 7, 8, 9
Step 1: Convert the matrix to row echelon form:
1, 2, 3 0, -3, -6 0, 0, 0
Step 2: Count the number of non-zero rows:
The rank of the matrix is 2.