For any augmented matrix of a system of linear equations, which of the following row transformations will not necessarily result in a matrix of an equivalent system?
(i) Adding to the elements of any row a multiple of the corresponding elements of another row.
(ii) Interchanging any two columns.
(iii) Multiplying the elements of any row by the corresponding elements of another row.
(iv) Multiplying the elements of any row by any nonzero number.
A) (ii)
B) (ii), (iii)
C) (ii), (iii), (iv)
D) (i), (iv)

Question

Quizplus · Accepted Answer

Interchanging any two columns changes the variables' positions, altering the system's solution set. Multiplying the elements of one row by the corresponding elements of another row is not a valid row operation for preserving the system's solutions, as it can fundamentally change the relationships between variables.

For Any Augmented Matrix of a System of Linear Equations