I want the solutions of these questions ASAP.

Question

Robert · Accepted Answer

3. (a) For the vector space V , we have suppose (x, y) ∈ V , then (ax, ay) ∈ V
for any a ∈ R.
For
V1 = {(x, y) : y ≤ 2x + 1}
We see (x, y) = (0,−6) ∈ V1, Hence if V1 is a vector space then
for a = −1, (ax, ay) = (−1 × 0,−1 × −6) should belong to V1.
But (ax, ay) = (0, 6) and this does not satisfy y ≤ 2x + 1. Hence
(0, 6) /∈ V1. Hence V1 is not a vector space.
For
V2 = {(x, y) : y > |x|}
We see (x, y) = (0, 1) ∈ V2, Hence if V2 is a vector space then for
a = −1, (ax, ay) = (−1 × 0,−1 × 1) should belong to V2. But
(ax, ay) = (0,−1) and this does not satisfy y > |x|. Hence (0,−1) /∈
V2. Hence V2 is not a vector space.
(b) Given equation of plane can be written as
5x− 2y + 3z = 11
Take
l1 : 5x− 2y = 11,

I want the solutions of these questions ASAP.

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment