Find the Rank [[1,-1,-3],[0,0,0]]

Problem

Rank*[[1,−1,−3],[0,0,0]]

Solution

1. Identify the matrix and the definition of rank. The rank of a matrix is the number of non-zero rows in its row echelon form.

2. Observe the current form of the matrix. The matrix is already in row echelon form because the second row consists entirely of zeros and the first row has a leading non-zero entry.

3. Count the number of non-zero rows. There is only one row that contains at least one non-zero element, which is the first row [1,−1,−3]

4. Determine the rank based on the count of non-zero rows. Since there is only one non-zero row, the rank is 1.

Final Answer

Rank*[[1,−1,−3],[0,0,0]]=1

Want more problems? Check here!