Find the Rank [[1,0,2/9],[0,1,-4/9],[0,0,0]]

Problem

rank(1)

Solution

1. Identify the matrix form. The given matrix is already in row-echelon form (REF) because the leading entries (pivots) of each row are to the right of the leading entries of the rows above them, and any rows of zeros are at the bottom.

2. Count the number of non-zero rows. In row-echelon form, the rank of a matrix is equal to the number of rows that contain at least one non-zero entry.

3. Determine the pivots. The first row has a pivot in the first column (1. The second row has a pivot in the second column (1. The third row consists entirely of zeros and contains no pivot.

4. Conclude the rank. Since there are 2 non-zero rows, the rank of the matrix is 2

Final Answer

rank(1)=2

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