How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R4?
A =[ 2 4 -1 12 ]
[ -2 -2 -2 -4 ]
[-4 0 -10 8 ]
[ 0 2 -3 11 ]
How many rows of A contain a pivot position? 0 A has rows which contain a pivot position. Does the equation Ax = b have a solution for each b in Rº? 0 b ] with b nonzero
A. Yes, because the reduced echelon form of A does not have a row of the form [0......0b)
B. Yes, because the columns of A do not span R4.
C. No, because A does not have a pivot position in every row.
D. No. because each b in R* is a linear combination of the columns of A.