Which of the following statements are true? There may be more than one true statement. A....

Which of the following statements are true? There may be more than one true statement.

A.

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

B.

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

C.

If the echelon form of the augmented matrix [A | b][A | b] has a leading entry in every row, then the equation Ax=b is inconsistent.

D.

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.

E.

If the columns of the matrix A form a linearly independent set, then the equation Ax=b is consistent.

F.

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

Expert Solution

Colby Messinger answered 1 month ago

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