Space Force 2

Let V1 ,..., VN be n vectors in R ^ n and let A n * n matrix whose columns are V1 ,..., VN
Put an X next to each statement below which the forces (v1 ,..., vn) is a basis of R ^ n

A) The SE (v1, ... vn) is indep


B) Span (v1 .. VN) is equal to R ^ n


C) The matrix A is equal to the line A, N * N Matrx ident


D) A matrix has an inverse

E) The number 0 is an eigenvalue of A

F) Ax = b is a solution for every vector b in R ^ n


G) is equal to the diagonal line


H) Sun (null space of A n) =


I) Det (A) = 0

J) The characteristic polynomial of A divides R

A) X
B) X
C) X
D) X
E)
F) X
G)
H)
I)
J)

Only 5 above

(Considering the VK are the zero vector, then A has all its entries to 0 and therefore A satisfies all the conditions E, G, H, I, J, but the set of vectors VK n ' is not a base)