Find the Rank [[1,2,-1],[-1,4,1],[0,6,0]]

Problem

rank(1)

Solution

1. Set up the matrix A for row reduction.

A=[[1,2,−1],[−1,4,1],[0,6,0]]

2. Eliminate the first element of the second row by adding the first row to the second row ((R_2)←(R_2)+(R_1).

[[1,2,−1],[0,6,0],[0,6,0]]

3. Eliminate the second row's duplicate by subtracting the second row from the third row ((R_3)←(R_3)−(R_2).

[[1,2,−1],[0,6,0],[0,0,0]]

4. Identify the number of non-zero rows in the row echelon form to determine the rank.

Number of non-zero rows=2

Final Answer

rank(1)=2

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