1) Let V be the set of all ordered pairs (x, y). where x, y are...

 

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1) Let V be the set of all ordered pairs (x, y). where x, y are real numbers. Let a- (x, y,) and b- (x,. y) be two elements in V. Define the addition as a +b = (x. y) +(*. )-(2x,-3x,, - y) and the scalar multiplication as a (x,, y,) = (ax, /3,a y,/3). Show that V is not a vector space. Which of the properties are not satisfied? 1) Let V be the set of all ordered pairs (x, y). where x, y are real numbers. Let a- (x, y,) and b- (x,. y) be two elements in V. Define the addition as a +b = (x. y) +(*. )-(2x,-3x,, - y) and the scalar multiplication as a (x,, y,) = (ax, /3,a y,/3). Show that V is not a vector space. Which of the properties are not satisfied?