Find the Rank [[1,-4,2],[2,1,0],[5,-2,2]]

Problem

Rank*[[1,−4,2],[2,1,0],[5,−2,2]]

Solution

1. Set up the matrix A for row reduction.

A=[[1,−4,2],[2,1,0],[5,−2,2]]

2. Eliminate the first entries of the second and third rows using the first row.

(R_2)→(R_2)−2*(R_1)

(R_3)→(R_3)−5*(R_1)

[[1,−4,2],[0,9,−4],[0,18,−8]]

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

(R_3)→(R_3)−2*(R_2)

[[1,−4,2],[0,9,−4],[0,0,0]]

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

Number of non-zero rows=2

Final Answer

Rank*[[1,−4,2],[2,1,0],[5,−2,2]]=2

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