Question

The 0 vecter is a vecter space r4 is

Answer 1

Your question is:

Zero vector in vector space R4 is :

Answer:

(0,0,0,0)

Every vector in vector space R4 can be represented as

$\sf (v_1,v_2,v_3,v_4)=v$

We have to find,

v+x=x+v=v

Now, In Coordinate notation, $\sf (v_1,v_2,v_3,v_4)+(x_1+x_2+x_3+x_4) \\\\\sf </p><p>=(v_1+x_1), (v_2+x_2),(v_3+x_3),(v_4+x_4) \\\\\sf </p><p>= (v_1,v_2,v_3,v_4)</p><p>$

$Now, \\\\\sf v_1+x_1=v_1 \\\\\sf v_2+x_2=v_2 \\\\\sf </p><p>v_3+x_3=v_3 \\\\\sf v_4+x_4= v_4 \\\\\sf$

From properties of addition in R, we know that.... $\sf x_1=x_2=x_3=x_4=0$

So, vector x is (0,0,0,0)