Question

Describe the possible echelon forms of a nonzero 2 x 2 matrix. Use the symbols , *, and 0, as in the first part of Example 1.

Answer 1

The possible echelon forms of a nonzero 2 x 2 matrix can be described using symbols * , and 0. There are three possible echelon forms: [* ,*] [ ,0], [0,*] [ ,*], and [0,0] [ ,*].

Step-by-step explanation:

The possible echelon forms of a nonzero 2 x 2 matrix can be described using the symbols *, 0, and ,. There are three possible echelon forms:

1. [*, *]
   [ , 0]
2. [0, *]
   [ , *]
3. [0, 0]
   [ , *]

In the first echelon form, the first row can have any non-zero entries and the second row is completely filled with zeros except for the last column. In the second echelon form, the first row is filled with zeros except for the last entry, which can be any non-zero value, and the second row can have any entries. In the third echelon form, both rows are filled with zeros except for the last column, which can have any non-zero entry.