Find Reduced Row Echelon Form [[1,0,0,3],[0,1,-5,7],[0,0,0,0]]

Problem

[[1,0,0,3],[0,1,−5,7],[0,0,0,0]]

Solution

1. Identify the leading entries (pivots) in each row. The first row has a leading 1 in the first column. The second row has a leading 1 in the second column. The third row consists entirely of zeros.

2. Check the conditions for Reduced Row Echelon Form (RREF). A matrix is in RREF if the first non-zero entry in every row is 1 these leading 1 move to the right as you go down rows, any row of zeros is at the bottom, and each column containing a leading 1 has zeros everywhere else.

3. Verify the columns. Column 1 has a leading 1 and zeros elsewhere. Column 2 has a leading 1 and zeros elsewhere. The third row is already at the bottom.

4. Conclude that the matrix already satisfies all requirements for Reduced Row Echelon Form. No further row operations are necessary.

Final Answer

rref*[[1,0,0,3],[0,1,−5,7],[0,0,0,0]]=[[1,0,0,3],[0,1,−5,7],[0,0,0,0]]

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