Find the Rank [[1,2,3],[0,1,2],[2,5,8]]

Problem

rank(1)

Solution

1. Set up the matrix A representing the given system.

A=[[1,2,3],[0,1,2],[2,5,8]]

2. Perform row operations to reach row echelon form by eliminating the first element of the third row using the first row.

(R_3)→(R_3)−2*(R_1)

[[1,2,3],[0,1,2],[0,1,2]]

3. Eliminate the second element of the third row using the second row.

(R_3)→(R_3)−(R_2)

[[1,2,3],[0,1,2],[0,0,0]]

4. Identify the number of non-zero rows in the row echelon form, which corresponds to the rank of the matrix.

Number of non-zero rows=2

Final Answer

rank(1)=2

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