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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Definitions:

Binomial Distribution

A probability distribution that summarizes the likelihood that a value will take one of two independent states under a given number of parameters.

At Most One

Indicates a restriction or condition where the maximum number of occurrences or instances is one.

Standard Deviation

A statistical measure of the dispersion or variability of a set of numbers, indicating the average distance from the mean.

Montana Highways

Refers to the network of state and interstate highways that crisscross the state of Montana, serving as important transportation routes.