# Dimension of matrix

1. May 23, 2012

### sharks

1. The problem statement, all variables and given/known data
$$A= \begin{bmatrix}1 & 1 & 1 & 1 \\ 2 & 1 & 0 & -1 \\ 3 & 4 & 5 & 6 \\ -1 &2 &1&0 \end{bmatrix}$$Determine the dimension of A and give a set of basis vectors for A.

2. Relevant equations
Dimension of matrix, ref form of matrix.

3. The attempt at a solution
I reduced the matrix to row echelon form and then the dimension = rank of matrix. Is that correct? I am quite confused about what dimension means. In a 4x4 matrix, maybe dimension is 16? or is it the number of non-zero matrix elements?

2. May 23, 2012

### sid9221

Easy way to remember it is:

# of columns - # of non zero rows in rref

3. May 23, 2012

### sharks

So, the dimension of A is the rank of the matrix A?

4. May 23, 2012

### HallsofIvy

Staff Emeritus
Yes. In fact, I would consider the term "dimension of a matrix" very strange. The rank of a matrix is the dimension of the image of the matrix.

5. May 23, 2012

### sid9221

I think by dimension you mean "nullity" cause our lecturer also used "dimension of a matrix" which was confusing when studying from other sources.