A subspace of Rn is any set H in Rn that has three properties: a) The...

A subspace of Rⁿ is any set H in Rⁿ that has three properties:

a) The zero vector is in H.
b) For each u and v in H, the sum u + v is in H.
c) For each u in H and each scalar c, the vector cu is in H.

Explain which property is not valid in one of the following regions (use a specific counterexample in your response):

a) Octant I
b) Octant I and IV
c) Octants I, II, III, and IV
d) Octants I and VII
e) Octants II and VI
f) Octants I and II
g) Octants II and III
h) Octants VII and VIII
i) Octants V, VI, VII, and VIII
j) Octants II and VII

Assume the bounding planes are included in the regions described above.

Expert Solution

Colby Messinger answered 2 years ago

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