The row instruction is written next to Row 1, meaning that we are to replace Row 1 according to the instruction, 3 R₁ - 2 R₂. In words, this means

"Replace Row 1 (the top row) by 3 times the top minus 2 times the bottom."

Now, rewrite the top row, going from left to right, as follows:

First entry:

3(top) - 2(bottom) = 3(1) - 2(3) = 3 - 6 = -3.

Therefore, the first entry is -3.

Second entry:

3(top) - 2(bottom) = 3(-2) - 2(0) = -6 - 0 = -6.

This is the second entry.

Third entry:

3(top) - 2(bottom) = 3(5) - 2(9) = 15 - 18 = -3.

Thus, the new first row is

[-3   -6   -3].

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