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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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