Step-by-step explanation
A matrix in row echelon form is a matrix that is the result of a process of Gaussian elimination. This means that operations were performed over the rows of a previous matrix until all the coefficients below its main diagonal were 0.
A matrix in reduced row echelon form meets a few properties:
- The leading entry of each non zero row (i.e. the first non-zero number counting from the left) has to be 1.
- Each column containing a leading entry 1 must have zeros in all of its other entries.
A 2x2 matrix that meets all these properties (i.e. is written in reduced row echelon form) will then look like this:
Where a and b can be any number.
Answer
As you can see there's only one option with a matrix that has the same form as the one I wrote above, option D. Then the answer is option D.