00:01
We are asked to write s in set notation.
00:04
And we do this by using the information in the problem, write that s is a set of vectors x, y, z, and r3, such that z is equal to 3x, and y equals 2x, and then close the set notation.
00:35
So this is our set notation.
00:39
And now we need to determine whether s is a subspace of v.
00:44
If s is a subspace of v, we need to show that s is closed under addition, and s is closed under scalar multiplication.
00:55
And there's also a quick check that if the zero vector does not exist in the subset s, then s is not a subspace.
01:03
So we'll check the zero vector first.
01:10
Zero vector check.
01:16
So we'll have some vector in our subset, which is equal to x, and this y, which is 2x, and z, which is 3x.
01:28
And if we set, x equals 0, x equals 0, and we get the vector 0, 2 times 0, 3 times 0, which is equal to the 0 vector.
01:48
So the 0 vector does exist...