00:01
We have been given a ,b ,c are real numbers and the subset of r3 consisting of vectors of the form abc where abc equal to 0.
00:29
We have to find if the set is a subspace or not.
00:41
Now we see that the zero vector in r3 is 000 and this vector satisfy the condition abc equal to 0.
01:01
So this is in the subset and now let a1 ,b1 ,c1 and a2 ,b2 ,c2 be two vectors in the subset.
01:23
We need to show that u plus v is also in the subset.
01:33
Now u plus v is equal to a1 plus b1, a2 plus b2, a1 plus a2, b1 plus b2, c1 plus c2.
01:51
Now since abc equal to 0 for both u and v, we have a1 ,b1 ,c1 equal to 0 and a2 ,b2 ,c2 equal to 0.
02:07
If either a1 equal to 0 or a2 equal to 0 then a1 plus a2 equal to 0 and the condition abc equal to 0 is satisfied for u plus v and if a1 is not equal to 0 and a2 is not equal to 0 then either b1 equal to 0 or c1 equal to 0 for u and either b2 equal to 0 or c2 equal to 0 for v...