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(Solved): 4. The Set V = {(x, Y)| X And Y Are Positive R} Is A Vector Space Under The Addtion: (X1, 71) + (x2, ...

4. The set V = {(x, y)| x and y are positive R} is a vector space under the Addtion: (X1, 71) + (x2, y2) = (x1x2, Y.Y2) & Sca

(Axiom 5) Show c(u + v) = cu + cv for all u, V EV and all real numbers c: 6 points

(Axiom 6 Show (C + d) v = CV + dv for all ve V and all real numbers c and d: 5 points

4. The set V = {(x, y)| x and y are positive R} is a vector space under the Addtion: (X1, 71) + (x2, y2) = (x1x2, Y.Y2) & Scalar Multiplication: c(x, y) = (x^,y). For axioms 1, 2, and 5: u = (x1, y?), v = (X2, y2), and w = (x3, Y3); for axioms 3,4,6,7, and 8: let v = (x,y). (40 points) (Axiom 5) Show c(u + v) = cu + cv for all u, V EV and all real numbers c: 6 points (Axiom 6 Show (C + d) v = CV + dv for all ve V and all real numbers c and d: 5 points

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