Determine if the described set is a subspace. The subset of Rn (n even) consisting of vectors of the form v = v1 vn , such that v1 − v2 + v3 − v4 + v5 − − vn = 0. The set is a subspace. The set is not a subspace.

The set is a subspace

Step-by-step explanation:

We need to check 3 things: whether the 0 vector is in the set, whether the sum of 2 elements of the set is an element of the set and whether the product of an element of the set for a real scalar is an element of the set.

Yes: the 0 vector (0, 0, ..., 0) satysfies the set property: 0-0+0-0-0 = 0.

Yes: Note that (v1+w1)-(v2+w2)+(v3+w3)- - (vn+wn) = v1-v1+v3 - ... - vn + w1 - w2 + w3 - ... - wn = 0+0 = 0.

Yes: By taking r as common factor, we have rv1 - rv2 + rv3 - ... - rvn = r * (v1-v2+v3 - ... - vn) = r*0 = 0.

Thus, the described set is effectively a subspace.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1