00:01
Hello friends, on this question we are given with the set s equal to 1, 1, 0, 1, 0, 1, 0, 1, 1, 1 be the subset of vector space f3 to prove f equal to r.
00:13
So we take the let x equal to 1, 1, 0 plus y into 1, 0, 1 plus equal to 0, double 1 that is 1, 1 which equal to 0.
00:22
So simplifying that we get x plus y equal to 0 which marked as equation 1, x plus z equal to 0 which marked as equation number 2, y plus z equal to 0 which marked as equation number 3.
00:32
Adding those equation we get yx plus y plus z which is equal to 0 which marked as equation number 4.
00:38
From subtracting 1, 2, 3 from 4 we get x equal to y equal to z equal to 0.
00:43
Therefore, hence the set that is 1, 1, 0, 1, 0, 1, 0, 1, 1 is linearly dependent.
00:51
We completed the first part.
00:52
We moved to the second part that is if f characteristic is 2, then s is a linear dependent.
00:56
So we have to show that s is linear dependent.
00:59
Let us take the set similarly from the set s.
01:02
It is considered in a 2d space then it becomes the plane as the op and oq and or that is the three points then equation of the plane that is ax plus by plus cz which is equal to d...