Determine the element of V that represents the zero vector 0 (i.e., determine the “value” of 0 in V ). b) Verify that k0 = 0 (i.e., show that your previous answer satisfies this axiom). c) Let u = (u1, u2) be in V. Find the value of −u such that u + (−u) = 0. (d) Verify that (−1)u = −u holds for your choice of −u.
Please explain!
Let V be the set of all ordered pairs of real numbers,(x, y), and consider the following
addition and scalar multiplication operations on u = (u1, u2) and v = (v1, v2):
u + v = (u1v1, u2v2) and ku = k(u, u2) = (uk1, uk2)
Given that V is a
and scalar multiplication), whose elements satisfy the ten axioms, answer the following for elements u = (u1, u2) where u1 =/= 0 and u2 =/= 0:
a) Determine the element of V that represents the zero vector 0 (i.e., determine the “value” of 0 in
V ).
b) Verify that k0 = 0 (i.e., show that your previous answer satisfies this axiom).
c) Let u = (u1, u2) be in V. Find the value of −u such that u + (−u) = 0.
(d) Verify that (−1)u = −u holds for your choice of −u.
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