MATH 240 MIDTERM 1 QUESTIONS AND CORRECT ANSWERS

MATH 240 MIDTERM 1 QUESTIONS
AND CORRECT ANSWERS
Span{v} ✅✅ANSW-line through origin



span{u,v} ✅✅ANSW-plane through origin



True/False: THe set Span{u,v} is always visualized as a plan through the origin ✅✅ANSW-False bc
u and v could be scalar multiples so just a line



Having a pivot in the augmentation column implies ✅✅ANSW-solution set is empty/inconsistent



If the only solution to Ax=0 is the zero vector, then ✅✅ANSW-the solution set is Span{0}



How many vectors are in Span{a1,a2,a3} ✅✅ANSW-infinitely many bc infinitely many linear
combinations bc infinite choices for scalar multiples



Vector u is in the plane spanned by the columns of A if and only if U is a linear combination of the
columns of A ✅✅ANSW-This happens, if and only if the equation Ax=u has a solution



If the augmented matrices of two linear systems are row equivalent, then ✅✅ANSW-the two
systems have the same solution set



Each matrix is row equivalent to one and only one ✅✅ANSW-reduced echelon matrix



If there are free variables, then ✅✅ANSW-solution is not unique and there are infinitely many
solutions



Is vector b in Span{v1,...vp} is asking ✅✅ANSW-whether x1v1+x2v2+...xpVp=b has a solution



Zero vector always in ✅✅ANSW-Span{v1,....vp}