Which of the following statements are true for a design matrix X ∈ Rn×d with d > n? (The rows are n sample points and the columns represent d features.)

• A. least-squares linear regression computes the weights w = (xtx)−1 xty
• B. the sample points are linearly separable
• C. x has exactly d − n eigenvectors with eigenvalue zero
• D. at least one principal component direction is orthogonal to a hyperplane that contains all the sample points