Question

Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns.

Answer 1

The possible echelon forms of a 2x2 matrix with linearly dependent columns are either a matrix with all zeros in the second column or a matrix with the second column being a multiple of the first column.

Step-by-step explanation:

The possible echelon forms of a 2x2 matrix with linearly dependent columns depend on the specific entries of the matrix. However, the general echelon form for such a matrix can be one of the following:

1. A matrix with all zeros in the second column, resulting in a rank of 1.
2. A matrix with the second column being a multiple of the first column, resulting in a rank of 1.

In both cases, the matrix will have linearly dependent columns, meaning one column can be obtained by multiplying the other column by a scalar.