Question

(1 point) Let A-0 -2 3 Find a basis of nullspace(A). Answer: To enter a basis into WeBWorK, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 21 , then you would enter [1,2,3],11,1,1] into the answer blank.

Answer 1

matrix is

0	4	6
0	-2	-3
0	6	9

convert into Reduced Row Eschelon Form...

Divide row1 by 4

0	1	3/2
0	-2	-3
0	6	9

Add (2 * row1) to row2

0	1	3/2
0	0	0
0	6	9

Add (-6 * row1) to row3

0	1	3/2
0	0	0
0	0	0

reduced matrix is

$x=x$ .......................free variable

$y+\frac{3}{2}z=0................y=-\frac{3}{2}z$

$z=z$ .......................free variable

.

solution is

$\begin{pmatrix}x\\ y\\ z\end{pmatrix}=x\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}+y\begin{pmatrix}0\\ -\frac{3}{2}\\ 1\end{pmatrix}$

null space are:

${\color{Red} \begin{pmatrix}1\\ 0\\ 0\end{pmatrix},\:\begin{pmatrix}0\\ -\frac{3}{2}\\ 1\end{pmatrix}}$