Column space

  • Thread starter FourierX
  • Start date
  • #1
73
0

Homework Statement



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

[1 -3]
[2 5]


Homework Equations



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

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.
 

Answers and Replies

  • #2
135
0
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;

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

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
73
0
Is the

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

or

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

[tex]

\begin{pmatrix}
1; -3\\
2; 5
\end{pmatrix}
[/tex]
 
  • #4
73
0
thanks, i resolved it!
 
  • #5
135
0
Oh yea sorry I read your matrix backwards accidentally. Glad you got it.
 

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