thanks Consider the set V of all ordered pairs of real numbers, with the operati

Question

thanks

Consider the set V of all ordered pairs of real numbers, with the operations (a, b) oplus (c, d) = (ac, bd) and k odot (a, b) = (ka, kb). This set is NOT a vector space. Which of the following fail to hold? There exists an element 0 in V such that u oplus 0 = 0 oplus u = u for any u in V. u oplus (v oplus w) = (v oplus v) oplus w for any u, v, w in V. (s + t) odot u = s odot u oplus t odot u for any u in V and real numbers s and t. s odot (t odot u) = (st) odot u for any u in V real numbers s and t.

Explanation / Answer

Option 2 fails to hold as it does not satisfies any of the properties of vector space and is not associative .

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