60.2K

Verified Solution

Link Copied!

1----

. Is the statement? "Elementary row operations on an augmentedmatrix never change the solution set of the associated linear?system" true or? false? Explain.

A.

?True, because elementary row operations are always applied toan augmented matrix after the solution has been found.

B.

?False, because the elementary row operations make a systeminconsistent.

C.

?True, because the elementary row operations replace a systemwith an equivalent system.

D.

?False, because the elementary row operations augment the numberof rows and columns of a matrix.

2---

Indicate whether the statements given in parts? (a) through? (d)are true or false and justify the answer.

a. Is the statement? "Every elementary row operation is?reversible" true or? false? Explain.

A.

?False, because only interchanging is a reversible rowoperation.

B.

?True, because interchanging can be reversed by? scaling, andscaling can be reversed by replacement.

C.

?False, because only scaling and interchanging are reversiblerow operations.

D.

?True, because? replacement, interchanging, and scaling are allreversible.

3----

In parts ?(a) through? (e) below, mark the statement True orFalse. Justify each answer.

a. The echelon form of a matrix is unique. Choose the correctanswer below.

A.

The statement is true. The echelon form of a matrix is always?unique, but the reduced echelon form of a matrix might not beunique.

B.

The statement is true. Neither the echelon form nor the reducedechelon form of a matrix are unique. They depend on the rowoperations performed.

C.

The statement is false. The echelon form of a matrix is not?unique, but the reduced echelon form is unique.

D.

The statement is false. Both the echelon form and the reducedechelon form of a matrix are unique. They are the same regardlessof the chosen row operations.