a. Every matrix equation Ax = b corresponds to a vector equation with the same solution set.
b. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x.
c. 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 ].
d. If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A.
e. If the augmented matrix [A b ] has a pivot position in every row, then the equation Ax = b is inconsistent.
f. If A is an m × n matrix whose columns do not span ℝm, then the equation Ax = b is inconsistent for some b in ℝm.
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