Show that the dimension of the set $\{(x, y, z) | 2x − 3y + z = 0\}$ is two by exhibiting a basis for the null space
Show that the dimension of the set $\{(x, y, z) | 2x − 3y + z = 0\}$ is two by exhibiting a basis for the null space
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0It would be much better for you to tell us the progress you've made and where you came across a problem. Problem like this should be elaborated in most of Linear Algebra books. – 2017-01-24
1 Answers
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We have $2x-3y+z=0$ i.e $z=3y-2x$.
Now $(x,y,z)=(x,y,3y-2x)=(x,0,-2x)+(0,y,3y)=x(1,0,-2)+y(0,1,3).$
So, the basis for null space is $\{(1,0,-2),(0,1,3)\}$ i.e nullity is $2$ .