Final answer:
The row operation -2r1 + r2 → r3 on the given matrix is mistakenly described and should involve adding -2 times the first row to the second row, with the result replacing the third row. The correct resulting matrix after the row operation is | 3 12 6 102 |, | 6 18 6 162 |, | -6 -6 -6 -84 |. However, the provided option for r3 is incorrect.
Step-by-step explanation:
The student's question involves performing a row operation on a given matrix that represents tickets sold and their total cost for three performances. To apply the described row operation, -2 times row 1 (r1) must be added to row 2 (r2), and this result will replace row 3 (r3). Below are the step-by-step calculations:
- First row (r1): | 3 12 6 102 |
- Multiply r1 by -2: | -6 -24 -12 -204 |
- Second row (r2): | 6 18 6 162 |
- Add the result of -2*r1 to r2: | 0 -6 -6 -42 |
- This result (| 0 -6 -6 -42 |) will replace the third row.
The resulting matrix after the row operation of -2r1 + r2 → r3 will be:
1) 3 12 6 102
2) 6 18 6 162
3) 0 -6 -6 -42
However, there seems to be a misinterpretation in the original question since r2 is not used in the operation. If we use r2 correctly in the operation and the result is to replace r3, then the correct result would be:
1) 3 12 6 102
2) 6 18 6 162
3) -6 -6 -6 -84
The values provided in option 4) -6 -6 -6 -60 do not match our calculation and therefore, may be incorrect.