Simplify the Matrix

Problem

[[1,−2,2,4,0,−8],[0,0,1,0,0,9],[0,0,0,1,0,5],[0,0,0,0,0,0]]

Solution

1. Identify the pivot positions in the matrix. The pivots are located at row 1 column 1, row 2 column 3, and row 3 column 4.

2. Eliminate the entry above the third pivot (row 3, column 4) by performing the row operation (R_1)→(R_1)−4*(R_3)

[[1,−2,2,0,0,−28],[0,0,1,0,0,9],[0,0,0,1,0,5],[0,0,0,0,0,0]]

3. Eliminate the entry above the second pivot (row 2, column 3) by performing the row operation (R_1)→(R_1)−2*(R_2)

[[1,−2,0,0,0,−46],[0,0,1,0,0,9],[0,0,0,1,0,5],[0,0,0,0,0,0]]

Final Answer

[[1,−2,2,4,0,−8],[0,0,1,0,0,9],[0,0,0,1,0,5],[0,0,0,0,0,0]]=[[1,−2,0,0,0,−46],[0,0,1,0,0,9],[0,0,0,1,0,5],[0,0,0,0,0,0]]

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