A conceptual question concerning with the Span of Matrix

[flyingpig]

Homework Statement

Let A = matrix of size m x n, where m can or cannot be equal to n. The matrix is Rref(A) is in a "perfect staircase" in which exists a unique solution. What can you comment about the Span of the column and row of this matrix?

The Attempt at a Solution

I am honestly stuck...

I am guessing it can span and the columns must be linearly dependent since we have a unique solution. But the row part confuses me

 

[Mark44]

Homework Statement

Let A = matrix of size m x n, where m can or cannot be equal to n. The matrix is Rref(A) is in a "perfect staircase" in which exists a unique solution. What can you comment about the Span of the column and row of this matrix?

The Attempt at a Solution

I am honestly stuck...

I am guessing it can span and the columns must be linearly dependent since we have a unique solution. But the row part confuses me

What does '"it" can span' mean? You should strive to make statements that are more meaningful, and in particular minimize the use of "it" unless the antecedent (what "it" refers to) is crystal clear.

I'm not sure what "perfect staircase" means. I've never seen that term used to describe a matrix in RREF form.

Is these matrices in perfect staircase form?
$$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$

$$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\\ 0 & 0 & 0 \end{bmatrix}$$

Is this one not in perfect staircase form?
$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\end{bmatrix}$$

 

[flyingpig]

When I mean "perfect staircase", I mean a unique solution, a pivot column in every row.

 

[Mark44]

I don't think that "perfect staircase" means "unique solution."
Here's the situtation for the three matrices I showed.
1. Unique solution (x = y = z = 0).
2. Unique solution (same as #1) but no pivot column in row 4.
3. Infinite number of solutions (x = 0, y = 0, z = 0, w = t, t in reals) and there is a pivot column in each row.