# Homework Help: Constructing a matrix from clues

1. Feb 21, 2010

### Identity

1. The problem statement, all variables and given/known data

Construct a matrix whose null space is spanned by $$\left[\begin{matrix} 1 \\ 1 \\ 0 \\ 0 \end{matrix}\right]$$ and $$\left[\begin{matrix} 1 \\ 0 \\ -1 \\ 1 \end{matrix}\right]$$ and whose column space is spanned by $$\left[\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}\right]$$ and $$\left[\begin{matrix} 0 \\ 1 \\ -1 \end{matrix}\right]$$

3. The attempt at a solution

I figured that it must be a 3x4 matrix, due to the dimensions of the column space and null space.

Apart from that, I'm not really sure where to go, I would greatly appreciate some help :)

2. Feb 21, 2010

### Staff: Mentor

Let's call your 3x4 matrix A. Each column of A must be a linear combination of (1 1 0)^T and (0 1 -1)^T.

Also, A*(1 1 0 0)^T = 0 and A*(1 0 -1 1)^T = 0, since those two vectors are in A's nullspace.

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