Find Reduced Row Echelon Form [[6,3,3,33],[3,3,0,15],[3,0,3,18]]

Problem

[[6,3,3,33],[3,3,0,15],[3,0,3,18]]

Solution

1. Divide the first row by 6 to create a leading 1 in the first column.

(R_1)→1/6*(R_1)

[[1,0.5,0.5,5.5],[3,3,0,15],[3,0,3,18]]

2. Eliminate the first column entries below the leading 1 by subtracting multiples of the first row from the second and third rows.

(R_2)→(R_2)−3*(R_1)

(R_3)→(R_3)−3*(R_1)

[[1,0.5,0.5,5.5],[0,1.5,−1.5,−1.5],[0,−1.5,1.5,1.5]]

3. Normalize the second row by dividing by 1.5 to create a leading 1 in the second column.

(R_2)→1/1.5*(R_2)

[[1,0.5,0.5,5.5],[0,1,−1,−1],[0,−1.5,1.5,1.5]]

4. Eliminate the second column entries above and below the leading 1 in the second row.

(R_1)→(R_1)−0.5*(R_2)

(R_3)→(R_3)+1.5*(R_2)

[[1,0,1,6],[0,1,−1,−1],[0,0,0,0]]

Final Answer

rref*[[6,3,3,33],[3,3,0,15],[3,0,3,18]]=[[1,0,1,6],[0,1,−1,−1],[0,0,0,0]]

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