Find the Rank [[0,1,2],[3,4,5],[6,7,8]]

Problem

rank(0)

Solution

1. Write the matrix and identify the goal to find the number of linearly independent rows or columns using Gaussian elimination.

A=[[0,1,2],[3,4,5],[6,7,8]]

2. Swap rows to place a non-zero element in the first pivot position (row 1, column 1). Swap (R_1) and (R_2)

[[3,4,5],[0,1,2],[6,7,8]]

3. Eliminate the entry in the third row, first column by performing the row operation (R_3)→(R_3)−2*(R_1)

[[3,4,5],[0,1,2],[0,−1,−2]]

4. Eliminate the entry in the third row, second column by performing the row operation (R_3)→(R_3)+(R_2)

[[3,4,5],[0,1,2],[0,0,0]]

5. Identify the rank by counting the number of non-zero rows in the row echelon form. There are 2 non-zero rows.

rank(A)=2

Final Answer

rank(0)=2

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