Answer each of the statements that follow as true or false. In each case, explain or prove your answer.
Let x1, x2, . . . , xk be linearly independent vectors in Rn. If k < n and xk+1 is a vector that is not in Span(x1, x2, . . . , xk), then the vectors x1, x2, . . . , xk , xk+1 are linearly independent.
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