Let, $\displaystyle \ T =

\[\begin{bmatrix}

1 & 3 & -7 \\

2 & -1 & 0 \\

3 & -1 & -1\\

4 & -3 & -2

\end{bmatrix}

\] $

determine a basis for the (a) range space of $\displaystyle T $ and (b) null space of $\displaystyle T $

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- Oct 21st 2010, 10:17 PMSambitrange space and null space
Let, $\displaystyle \ T =

\[\begin{bmatrix}

1 & 3 & -7 \\

2 & -1 & 0 \\

3 & -1 & -1\\

4 & -3 & -2

\end{bmatrix}

\] $

determine a basis for the (a) range space of $\displaystyle T $ and (b) null space of $\displaystyle T $ - Oct 22nd 2010, 12:43 AMemakarov
This is a subject of Linear Algebra.

- Oct 23rd 2010, 06:08 AMSambit
ok. so how can i move it to there?

- Oct 23rd 2010, 06:33 AMHallsofIvy
**You**can't. Perhaps one of the moderators will do it.

In any case, you are expected to show what you have tried. What is the**definition**of "range" and "null space" of a matrix? - Oct 23rd 2010, 07:05 AMSambit
Null space of the matrix $\displaystyle T $ is the collection of $\displaystyle X$s where $\displaystyle TX = O $

and range of $\displaystyle T$ is the collection of all possible linear combinations of the column vectors of $\displaystyle T $