- #1

kosovo dave

Gold Member

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## Main Question or Discussion Point

So a question on my linear algebra homework asks for the dimensions of Nul(A) and Col(A).

Let A =

\begin{pmatrix}

-4 & -3\\

-1 &4\\

-3& -7

\end{pmatrix}

I row reduced the above matrix to

\begin{pmatrix}

1 & 0\\

0 & 1\\

\end{pmatrix}

Now, the T.A. for my section told us that to find the dimension of Nul(A) you look at the number of free variables in Nul(A). There are no free variables, so the dimension of Nul(A) is 0? What does this mean? I think I may be a little confused on what it means to find the dimension of a space. Why should the number of free variables in the null space tell you anything about the dimension of the null space?

Let A =

\begin{pmatrix}

-4 & -3\\

-1 &4\\

-3& -7

\end{pmatrix}

I row reduced the above matrix to

\begin{pmatrix}

1 & 0\\

0 & 1\\

\end{pmatrix}

Now, the T.A. for my section told us that to find the dimension of Nul(A) you look at the number of free variables in Nul(A). There are no free variables, so the dimension of Nul(A) is 0? What does this mean? I think I may be a little confused on what it means to find the dimension of a space. Why should the number of free variables in the null space tell you anything about the dimension of the null space?