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

Problem

rank(1)

Solution

1. Identify the matrix structure. The given matrix is already in row echelon form because all entries below the main diagonal are zero.

2. Count the number of non-zero rows. A row is considered non-zero if at least one element in the row is not zero.

3. Observe that the first row [1,1,2] is non-zero, the second row [0,−1,−4] is non-zero, and the third row [0,0,1] is non-zero.

4. Determine the rank. Since there are 3 linearly independent (non-zero) rows in this row echelon form matrix, the rank is 3.

Final Answer

rank(1)=3

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