A is an m X n matrix Check the true statements below The nul

A is an m X n matrix. Check the true statements below: The null space of A is the solution set of the equation Ax = 0. If the equation Ax = b is consistent, then ColA is R^m. The column space of A is the range of the mapping x rightarrow Ax. The null space of an m X n matrix is in R^m. ColA is the set of all vectors that can be written as Ax for some x The kernel of a linear transformation is a vector space.

Solution

A) The null space of A is the solution set of the equation Ax = 0. TRUE

B) If the equation Ax = b is consistent, then Col A is Rm. FALSE must be consistent for all b

C ) The column space of A is the set of all vectors that can be written as AX for some X. True

D) The null space of an m × n matrix is in R m. False. It’s actually Rn

E) Col A is the set of a vectors that can be written as Ax for some x. TRUE . Ax gives a linear combination of columns of A using x entries as weights.

F) The kernel of a linear transformation is a vector space. TRUE .We can prove this

by showing it is a subspace