Find the Rank s=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]

Problem

rank(2)

Solution

1. Write the matrix A representing the given system.

A=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]

2. Perform row operations to create zeros in the first column below the first entry. Subtract the first row from the second row ((R_2)−(R_1)→(R_2) and subtract the first row from the third row ((R_3)−(R_1)→(R_3).

[[2,4,6,4],[0,1,1,2],[0,−1,−1,−2]]

3. Eliminate the second entry in the third column by adding the second row to the third row ((R_3)+(R_2)→(R_3).

[[2,4,6,4],[0,1,1,2],[0,0,0,0]]

4. Identify the number of non-zero rows in the row echelon form of the matrix. There are 2 non-zero rows.

Final Answer

rank(2)=2

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