Find the Rank

Problem

rank(0)

Solution

1. Swap rows to place a non-zero leading entry in the first row. Swap (R_1) and (R_4)

[[1,7,17,3],[4,8,18,7],[10,18,40,17],[0,4,10,1]]

2. Eliminate the first column entries below the pivot. Perform (R_2)→(R_2)−4*(R_1) and (R_3)→(R_3)−10*(R_1)

[[1,7,17,3],[0,−20,−50,−5],[0,−52,−130,−13],[0,4,10,1]]

3. Simplify the rows by dividing (R_2) by −5

[[1,7,17,3],[0,4,10,1],[0,−52,−130,−13],[0,4,10,1]]

4. Eliminate the second column entries below the pivot. Perform (R_3)→(R_3)+13*(R_2) and (R_4)→(R_4)−(R_2)

[[1,7,17,3],[0,4,10,1],[0,0,0,0],[0,0,0,0]]

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

Final Answer

rank(0)=2

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