Find the Rank [[1,2,-1]]

Problem

Rank*[[1,2,−1]]

Solution

1. Identify the dimensions of the given matrix. The matrix A=[[1,2,−1]] is a 1×3 matrix, consisting of a single row.

2. Determine the number of non-zero rows. The rank of a matrix is defined as the number of linearly independent rows or columns, which corresponds to the number of non-zero rows in its row-echelon form.

3. Observe that the matrix is already in row-echelon form. Since there is at least one non-zero entry in the single row, the row is non-zero.

4. Conclude the rank based on the count of non-zero rows. There is exactly 1 non-zero row.

Final Answer

Rank*[[1,2,−1]]=1

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