Mark each statement True or False and explain why?

a. Elementary row operations on an agumented matrix never change the solution set of the associated linear system





b. Two matrices are row equivalent if they have the same number of rows





c. An inconsistent system has more than one solution





d. Two linear systems are equivalent if they have the same solution setMark each statement True or False and explain why?
a. True. Each row operation on an augmented matrix corresponds to performing some operation on the associated linear system which doesn't change the solution set.





b. False. For example,


[1 0]


[0 1]





and





[0 0]


[0 0]





are not row equivalent. You can show this lots of ways (for example, they are both in row-reduced echelon form, and each matrix is row equivalent to only one row-reduced echelon form).





c. False. An inconsistent system has zero solutions.





d. True. Two systems are said to be equivalent if each equation in each system can be written as a linear combination of the equations in the other system. This happens just when the two systems have the same solution set. (There is probably a theorem in your book which states this.)