Simplify the Matrix

Problem

[[1,0,0,3],[0,1,0,−1],[0,0,1,2],[0,0,0,0]]

Solution

1. Identify the current form of the matrix. The matrix is already in a specific configuration where the leading coefficient of each non-zero row is a 1 (a pivot), and each pivot is the only non-zero entry in its column.

2. Check for Reduced Row Echelon Form (RREF) criteria. A matrix is in RREF if all non-zero rows are above any rows of all zeros, the leading entry of each row is 1 and occurs to the right of the leading entry of the row above it, and each column containing a leading 1 has zeros everywhere else.

3. Conclude that the matrix is already fully simplified. Since it satisfies all the conditions for Reduced Row Echelon Form, no further row operations are required.

Final Answer

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

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