Describe the possible echelon forms of the standard matrix f

Describe the possible echelon forms of the standard matrix for a linear transformation T: R^2 Right Arrow R^3 when T is onto.

Solution

If the linear transformation T from R² to R³ is onto, then the columns of the standard matrix of T must span R³ . This means that the echelon forms of the standard matrix of the linear transformation T must have 3 pivot positions.