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. Repeat Exercise 5 for a nonzero 3 x 2 matrix.

Answer 1

The possible echelon forms of a nonzero 2 x 2 matrix can be represented using symbols , *, and 0. The forms depend on the arrangement of nonzero and zero elements in the matrix. The same principle applies to a nonzero 3 x 2 matrix.

Step-by-step explanation:

The echelon forms of a nonzero 2 x 2 matrix can be described using the symbols , *, and 0. These symbols represent different elements of the matrix.

One possible echelon form is when the first element of the first row is nonzero and the second element of the first row is zero. The second row can then have any elements. This form can be represented as:

[* , 0]
[*, *]

Another possible echelon form is when the first row is zero and the second row has nonzero elements. This form can be represented as:

[0 , *]
[*, *]

For a nonzero 3 x 2 matrix, the possible echelon forms can be described in a similar manner. One form is when the first element of the first row is nonzero and the remaining elements of that row are zero. The following rows can have any elements. This form can be represented as:

[*, 0]
[*, *]
[*, *]

Another form is when the first and second rows are nonzero and the third row is zero. This form can be represented as:

[*, *]
[*, *]
[0 , 0]