If 0 is in S a finite set of vectors then S must be linearly

If 0 is in S, a finite set of vectors, then S must be linearly dependent. 16. True False If the vectors v_1, V_2, ... v_n span R^4, then n must equal 4. 17. True False Any three vectors from R^2 must be linearly dependent. 18. True False For every subspace V of R^3 there is a 3times3 matrix A such that V = Col(A). 19. True False There exists a 5times4 matrix A such that Col(A) = R^5. 20. True False det(A) = det(RREF(A)). 21. True False A and RREF(A) have the same row space. 22. True False A and A^T have the same eigenvalues. 23. True False Let C = [1 2 3 4]. The set of all 2times2 matrices A such that AC = CA is a vector space.

Solution

15. True
16. False
17. True
18. False
19. True
20. False
21. False
22. True
23. True