Simplify the Matrix [[1,0,3,2],[0,0,0,0],[0,1,5,2]]

Problem

[[1,0,3,2],[0,0,0,0],[0,1,5,2]]

Solution

1. Identify the goal to simplify the matrix into its Reduced Row Echelon Form (RREF).

2. Swap the second and third rows to move the row of zeros to the bottom and place a leading entry in the second row.

(R_2)↔(R_3)

[[1,0,3,2],[0,1,5,2],[0,0,0,0]]

3. Check the conditions for Reduced Row Echelon Form: the first non-zero entry in each row (pivot) is 1, each pivot is to the right of the pivot above it, the columns containing pivots have zeros elsewhere, and any rows of zeros are at the bottom.

4. Conclude that the matrix is now in its simplest reduced form.

Final Answer

[[1,0,3,2],[0,0,0,0],[0,1,5,2]]=[[1,0,3,2],[0,1,5,2],[0,0,0,0]]

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