Simplify the Matrix [[1,-5,11],[0,0,0]]

Problem

[[1,−5,11],[0,0,0]]

Solution

1. Identify the current state of the matrix. The matrix is a 2×3 matrix.

2. Check for row echelon form (REF). A matrix is in row echelon form if all zero rows are at the bottom and the leading entry of each nonzero row is to the right of the leading entry of the row above it.

3. Observe the first row. The leading entry is 1 in the first column.

4. Observe the second row. The second row consists entirely of zeros and is located at the bottom of the matrix.

5. Conclude that the matrix is already in its simplest form, which is reduced row echelon form (RREF), because the leading coefficient of the only non-zero row is 1 and it is the only non-zero entry in its column.

Final Answer

[[1,−5,11],[0,0,0]]=[[1,−5,11],[0,0,0]]

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