Question

# Which of the following can be treated as an Elementary Row transformation.

A

Row 1 → Row 1 + Row 3

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B

Row 2 → Row 2 + 2 Row 1

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C

Row 2 → Row 2 + 2 Row 2

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D

Row 3 → Row 3 - Row 3

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Solution

## The correct options are A Row 1 → Row 1 + Row 3 B Row 2 → Row 2 + 2 Row 1 C Row 2 → Row 2 + 2 Row 2 We know the transformation that we can add a constant multiple of elements of a row to the corresponding elements to any other row. So, Row1 → Row1 + Row3 is correct Row 2 → Row 2 + 2 Row 1 is correct. We also know we can multiply every element of any row of a given matrix by a non zero number. So, Row2 → Row2 + 2 Row 2 which is same as Row2 → 3 Row2, 3 not equal to 0 so option c is correct Now, Row3 → Row3 - Row3 is same as Row3 → 0.Row 3 therefore option d is false. ∴options a, b, c are correct.

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