Question

Let w be the subset of vectors in r3 of the form

[a]
[b]
[c]
where b=3a+4c and ac≥0 Show W is NOT closed under addition (and thus, not a subspace) via counterexamples:

Answer 1

To show that vector addition is commutative, three vectors A, B, and C are chosen, and we confirm that the sum A + B + C is the same as C + A + B by computing both.

Step-by-step explanation:

The question is related to the commutativity property of vector addition in mathematics, which implies that vectors can be added in any order without affecting their sum. To demonstrate this, we can choose three vectors A, B, and C with different lengths and directions, and show that A + B + C equals C + A + B, one of the alternative orders. By computing and comparing the resulting vectors from both orders, we will find they are indeed the same, thus confirming the commutative property.