(true/false) 14.Every nonzero subspace has an orthonormal basis. 15.The result o

ID: 3115862 • Letter: #

Question

(true/false)

14.Every nonzero subspace has an orthonormal basis.

15.The result of applying the Gram-Schmidt procedure to a basis which is orthonormal is the same basis one started with.

16.If A, B are two matrices with compatible size, and A has rank 1 and B has rank 1, then rank(AB) 1.

17.If A , B have the same size then rank(A + B) > rank(A) + rank(B).

18.If A, B have the same size then rank(A + B) rank(A) + rank(B) .

19.If A is a nonzero n × 1 column vector then ATA is invertible.

20. There’s a vector b such that [123] x = b is not solvable.

21. Suppose that A^T A is invertible. Then so is A.

22. Suppose that the square matrix A^T A has linearly independent columns. Then A must be invertible.

14. yes it is true that every vector space has orthogonal basis

15 true .

16.false because rank(AB) = MIN( RANK A, rank B)

17. FALSE as always [ rank(A) + rank(B) rank(A + B)]

18. false as rank(A) + rank(B) rank(A + B)

19. true as ATA produces only one single entry which is non zero so it is naturally invertible.

20. false. for any real value of b , 123x is solvable.

21. true. A must be invertible to give A^T A as a invertible.

22. true.

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.