# Finding the basis for a 4x3 matrix

How do i find a basis for vector: \begin{matrix} 5 & 3 & 4 \\ 2 & 2 & -4 \\ 3 & 2 & 1 \\ -1 & 2 & 1\\ \end{matrix}

I know a basis of a vector A is a set of vectors which are linearly independent and span A. And a span of A is a set of vectors which can be linearly combined to create A

Do i just look randomly for vectors that span and are also linearly independent or is there a procedure to obtain them?

• What is a basis of a matrix? Incidentalyy, this is 4×3 matrix. – Bernard Feb 7 '17 at 22:23

If your vectors are the columns they are four dimensional but since you start with three your basis will have no more than three and will not be a basis for all of $R^4$.