Assume that vector b\displaystyle \vec{{b}}  is not a linear combination of vectors v1\displaystyle \vec{{v}}_{{1}} , v2\displaystyle \vec{{v}}_{{2}} , and v3\displaystyle \vec{{v}}_{{3}}.  Which of the following is true?  Assume all vectors are in Rn\displaystyle {R}^{{n}} .

 

a)  Ax=b\displaystyle {A}\vec{{x}}=\vec{{b}}  is consistent.

b)  The row reduced form of the augmented matrix [v1v2v3b]\displaystyle {\left[\vec{{v}}_{{1}}{\left|\vec{{v}}_{{2}}\right|}\vec{{v}}_{{3}}{\mid}\vec{{b}}\right]}  has no pivot in the right-most column.

c)  There is no solution to c1v1+c2v2+c3v3=b\displaystyle {c}_{{1}}\vec{{v}}_{{1}}+{c}_{{2}}\vec{{v}}_{{2}}+{c}_{{3}}\vec{{v}}_{{3}}=\vec{{b}}