Simplify the Matrix

Problem

[[1,0,8,0,−9],[0,1,7,0,9],[0,0,0,1,7],[0,0,0,0,−9]]

Solution

1. Identify the pivot in the fourth row, which is −9 at position (4,5)

2. Normalize the fourth row by dividing (R_4) by −9 to create a leading 1

(R_4)→−1/9*(R_4)

[[1,0,8,0,−9],[0,1,7,0,9],[0,0,0,1,7],[0,0,0,0,1]]

3. Eliminate the entries above the pivot in the fifth column to reach reduced row echelon form.

(R_1)→(R_1)+9*(R_4)

(R_2)→(R_2)−9*(R_4)

(R_3)→(R_3)−7*(R_4)

4. Simplify the resulting matrix.

[[1,0,8,0,0],[0,1,7,0,0],[0,0,0,1,0],[0,0,0,0,1]]

Final Answer

[[1,0,8,0,−9],[0,1,7,0,9],[0,0,0,1,7],[0,0,0,0,−9]]=[[1,0,8,0,0],[0,1,7,0,0],[0,0,0,1,0],[0,0,0,0,1]]

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