Simplify the Matrix [[0,1,6],[1,3,3],[3,8,3]]

Problem

[[0,1,6],[1,3,3],[3,8,3]]

Solution

1. Identify the goal of simplifying a matrix, which typically involves performing row operations to reach Row Echelon Form (REF) or Reduced Row Echelon Form (RREF).

2. Swap the first and second rows to place a non-zero leading entry (pivot) in the top-left position.

(R_1)↔(R_2)

[[1,3,3],[0,1,6],[3,8,3]]

3. Eliminate the entry in the third row, first column by subtracting 3 times the first row from the third row.

(R_3)−3*(R_1)→(R_3)

[[1,3,3],[0,1,6],[0,−1,−6]]

4. Eliminate the entry in the third row, second column by adding the second row to the third row.

(R_3)+(R_2)→(R_3)

[[1,3,3],[0,1,6],[0,0,0]]

5. Eliminate the entry in the first row, second column to reach Reduced Row Echelon Form by subtracting 3 times the second row from the first row.

(R_1)−3*(R_2)→(R_1)

[[1,0,−15],[0,1,6],[0,0,0]]

Final Answer

[[0,1,6],[1,3,3],[3,8,3]]=[[1,0,−15],[0,1,6],[0,0,0]]

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