Explain how you can or could determine that this solution set defines a plane in R4. Include in this explanation what the solution set may look like if it is not a plane in R4
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Vector Space Axioms Definition Let V be a set on which two operations, called vector addition and vector scalar multiplication, have been defined. If u and v are in V, the sum of u and v is denoted by u + v, and if k is a scalar, the scalar multiple of u is denoted by ku. If the following axioms true for all u, v and w in V and for all scalars k and l, then V is called a vector space and its objects in V are called vectors. 1) u + v is in V 2) u + v = v + u 3) (u + v) + w = u + (v + w) 4) 0 + v = v 5) v + (-v) = 0 6) ku is in V 7) k(u + v) = ku + kv 8) (k + l)u = ku + lu 9) k(lu) = (kl)(u) 10) 1v = v QUESTION Consider P4 be a set of all the point on a plane through the origin in R4. The general equation of a plane through the origin in R4 as follow aw + bx + cy + dz = 0 where a, b, c, and d are fixed constant and at least one is not zero. Show that P4 with the standard addition and scalar multiplication is a vector space.
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