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

Problem

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

Solution

1. Identify the current state of the matrix. The matrix is already in a specific form where the leading entries (pivots) are 1, and the columns containing these pivots have zeros in all other positions.

2. Check for Row Echelon Form (REF) requirements. All non-zero rows are above any rows of all zeros, and the leading entry of each row is to the right of the leading entry of the row above it.

3. Check for Reduced Row Echelon Form (RREF) requirements. Each leading entry is 1 and is the only non-zero entry in its column.

4. Conclude that the matrix is already in its simplest form, which is Reduced Row Echelon Form. No further row operations are necessary.

Final Answer

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

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