# Column space

1. Nov 22, 2008

### FourierX

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

Does b = [ 2 15 ]T lie in the column of the matrix A

[1 -3]
[2 5]

2. Relevant equations

a basis of CS(U) forms a basis for the corresponding columns for CS(A)

3. The attempt at a solution
I reduced the given matrix into row echelon form and determined its column space. But did not figure out if [2 15]T lies in the column space of A.

2. Nov 22, 2008

### jeffreydk

Your matrix A reduces to the identity matrix in reduced row echelon form; so then the column space is made up of all the columns of the original matrix;

$$\text{Col}(A)=\left\{ \begin{pmatrix} 1 \\ -3 \end{pmatrix} , \begin{pmatrix} 2 \\ 5 \end{pmatrix} \right\}$$

So does the vector they're asking lie in that space? In other words is it a linear combination of those vectors in the space?

3. Nov 22, 2008

### FourierX

Is the

$$\text{Col}(A)=\left\{ \begin{pmatrix} 1 \\ 2 \end{pmatrix} , \begin{pmatrix} -3 \\ 5 \end{pmatrix} \right\}$$

or

$$\text{Col}(A)=\left\{ \begin{pmatrix} 1 \\ -3 \end{pmatrix} , \begin{pmatrix} 2 \\ 5 \end{pmatrix} \right\}$$
?
The given matrix is

$$\begin{pmatrix} 1; -3\\ 2; 5 \end{pmatrix}$$

4. Nov 22, 2008

### FourierX

thanks, i resolved it!

5. Nov 22, 2008