Multiple choice

It is given that X1, X2, …..XM are M non-zero orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X1, X2, …XM , - XM is

  1. 2M

  2. M + 1

  3. M

  4. dependent on the choice of X1, X2, …..XM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If X_1, X_2, ..., X_M are orthogonal non-zero vectors, they are linearly independent and span an M-dimensional subspace. The set {-X_1, -X_2, ..., -X_M} consists of the same vectors scaled by -1, which doesn't add new dimensions - each -X_i is already in span{X_i}. Therefore span dimension remains M.

Keep practicing — related questions