Very often we use elementary transformations to find rank of matrices. Which of the following transformations are correct? I guess that only 1 is correct and 2, 3 are wrong. Am I right?
$R_2\to R_2-kR_3$
$R_2\to 2R_2-kR_3$
$R_2\to -R_2-kR_3$
2026-04-02 06:24:35.1775111075
Elementary tranformations in matrix
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1
They're not wrong, they're just a combination of two separate elementary row operations.
The 3 elementary row operations are (1) interchanging rows, (2) adding a multiple of one row to another, and (3) multiplying a row by a nonzero constant. Your number 2 and 3 are two row operations of types (2) and (3).