3. (10%) A matrix H for a linear block code is defined such that each vector v is a valid codeword if and only if Hv^T = 0.

Assume that $$H = \begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{bmatrix}$$.

(a) Is the vector \( v_{1} = [1\ 0\ 1\ 0\ 1\ 1] \) a valid codeword vector? Why or why not?

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