a. Every matrix equation Ax = b corresponds to a vector

Chapter 1, Problem 24E

(choose chapter or problem)

Problem 24E

a. Every matrix equation Ax = b corresponds to a vector equation with the same solution set.

b. If the equation Ax = b is consistent, then b is in the set spanned by the columns of A.

c. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x.

d. If the coefficient matrix A has a pivot position in every row, then the equation Ax = b is inconsistent.

e. The solution set of a linear system whose augmented matrix is [a1 a2 a3 b] is the same as the solution set of Ax = b, if A = [a1 a2 a3 b].

f. If A is an m × n matrix whose columns do not span ℝm, then the equation Ax = b is consistent for every b in ℝm.