Find Reduced Row Echelon Form [[1,0,0,7],[0,1,0,6],[0,0,1,7]]

Problem

[[1,0,0,7],[0,1,0,6],[0,0,1,7]]

Solution

1. Identify the current state of the matrix. The matrix is a 3×4 matrix where the first three columns form an identity matrix (I_3)

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 a 1 (leading 1, each leading 1 is to the right of the leading 1 in the row above it, all entries in a column containing a leading 1 are zero except for that 1 and any rows of all zeros are at the bottom.

3. Verify the leading ones. Row 1 has a leading 1 at column 1. Row 2 has a leading 1 at column 2. Row 3 has a leading 1 at column 3.

4. Verify the columns. Column 1 has a 1 in row 1 and zeros elsewhere. Column 2 has a 1 in row 2 and zeros elsewhere. Column 3 has a 1 in row 3 and zeros elsewhere.

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

Final Answer

rref*[[1,0,0,7],[0,1,0,6],[0,0,1,7]]=[[1,0,0,7],[0,1,0,6],[0,0,1,7]]

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