Consider ordered pairs from R2 and define addition as: (x1, x2)+(y1, y2) = (x1+2y1, x2 +2y2)...

 

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Consider ordered pairs from R2 and define addition as: (x1, x2)+(y1, y2) = (x1+2y1, x2 +2y2) and scalar multiplication as: a(x1, x2)=(2ax, ax2) Show your work for each of the following. (a) Does the above satisfy commutativity of addition: x+y=y+x? (b) Does the above satisfy associativity of addition: (x + y) +z = x + (y + z)? (c) Identity element of addition: 3ER2 so that Vx, x + B = x? (d) Does it satisfy the distributive law for scalar multiplication: Va ER, a(x + y) = ax + ay? (e) Identity element of multiplication: a ER so that Vx, ax = x? Consider ordered pairs from R2 and define addition as: (x1, x2)+(y1, y2) = (x1+2y1, x2 +2y2) and scalar multiplication as: a(x1, x2)=(2ax, ax2) Show your work for each of the following. (a) Does the above satisfy commutativity of addition: x+y=y+x? (b) Does the above satisfy associativity of addition: (x + y) +z = x + (y + z)? (c) Identity element of addition: 3ER2 so that Vx, x + B = x? (d) Does it satisfy the distributive law for scalar multiplication: Va ER, a(x + y) = ax + ay? (e) Identity element of multiplication: a ER so that Vx, ax = x?