Final answer:
The possible echelon forms of the standard matrix for a linear transformation t where t is onto depend on the dimensions of the input and output spaces.
Step-by-step explanation:
The possible echelon forms of the standard matrix for a linear transformation t where t is onto, depend on the dimensions of the input and output spaces. In general, if the input space has m dimensions and the output space has n dimensions, then the possible echelon forms of the standard matrix will have r pivot entries, where r is the rank of the matrix.
If m = n = r, then the echelon form will be an m x n identity matrix. If m > n, then the echelon form will have r rows of pivot entries followed by m - r rows of zeros. If m < n, then the echelon form will have r columns of pivot entries followed by n - r columns of zeros.