Determine whether the statement is True or False. Justify your answer:If u is a vector in a vector space V, then (−1)u is the same as the negative of u.
The statement is true
The statement is true.
To justify this, let’s recall the definition of scalar multiplication in a vector space. In a vector space, scalar multiplication involves multiplying a vector by a scalar (which is a number).
The negative of a vector, denoted as -u, is obtained by multiplying the vector u by -1. This means that (-1)u is indeed the negative of u.
To understand why this is the case, let’s consider an example. Suppose we have a vector u = (2, 4). If we multiply this vector u by -1, we get (-1)u = (-1)(2, 4) = (-2, -4). We can clearly see that (-2, -4) is the negative of the original vector (2, 4).
This holds true for any vector u in a vector space V. Therefore, the statement is true.
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