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GATE ECE 2007 | Question-21


It is given that $X_{1}, X_{2}, \cdots X_{M}$ are $M$ non-zero, orthogonal vectors. The dimension of the vector space spanned by the $2 M$ vectors $X_{1}, X_{2}, \cdots X_{M},-X_{1},-X_{2}, \cdots-X_{M}$ is

  1. $2 M$
  2. $M+1$
  3. $M$
  4. dependent on the choice of $X_{1}, X_{2}, \cdots X_{M}$
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