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If $f = {(a, 1), (b, - 2), (c, 3)}, g = {(a, - 2), (b, 0), (c, 1)}$ , then $f^{2} + g^{2} =$

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{(a, 3), (b, - 2), (c, 2)}

{(a, - 4), (b, - 4), (c, 9)}

{(a, 5), (b, 4), (c, 10)}

{(a, - 1), (b, - 2), (c, 4)}

answer is D.

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Detailed Solution

f^{2} + g^{2} = {(a, {(1)}^{2} + {(- 2)}^{2}), (b, {(- 2)}^{2} + {(0)}^{2}), (c, {(3)}^{2} + {(1)}^{2})}

$= {(a, 5), (b, 4), (c, 10)}$

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