For Any Augmented Matrix of a System of Linear Equations

question 349

Multiple Choice

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) (i), (iv)
• B) (ii), (iii), (iv)
• C) (ii), (iii)
• D) (ii)

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