Question
thanks
Which of the following statements are true? A. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. B. The equation Ax = b is consistent if the augmented matrix [A b] has a pivot position in every row. C. If the augmented matrix [A b] has a pivot position in every row, then the equation Ax = b is inconsistent. D. If the columns of an m times n matrix A span R^m, then the equation Ax = b is consistent for each b in R^m. E. The solution set of a linear system whose augmented matrix is [a_1 a_2 a_3 b] is the same as the solution set of Ax = b, if A = [a_1 a_2 a_3]. F. If A is an m times n matrix and if the equation Ax = b is inconsistent for some b in R^m, then A cannot have a pivot position in every row.
Explanation / Answer
A) True.
B) False.
C) False.
D) True.
E) True.
F) True.
