Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

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One thing that we can do is, we can add a multiple of one row to another, and we can add a multiple of one column to another. What I want to do is I want to try and get a zero right here, by adding -2 times this last column to this column. So, that’s going to change the middle column but it won’t change the first or last. So I can write those down as they are. 2 3 6, and –2 times this is -4, plus 4 is 0. -2 times 3 is 6,, plus 9 is 3. -2 times 6 is -12, plus 8 is -4. So this column is -2 times C3 plus C2.

Let’s see if I can do that again, because if I have two zeros in one row, it’s going to be really easy to evaluate the determinant. Let’s try to get a zero right here. I’ll get that by multiplying this column by -4, and adding it to the first column. The second and third columns will stay the same; 0 3 -4, 2 3 6. And again I’m adding -4 times this column to this one. So -4 times 2 is -8 plus 8, 0. -4 times 3 is -12, plus 3, -9. -4 times 6 is -24, minus 2 is -26.

I got what I wanted. I have two zeros here. It’s going to be really easy to expand along this top row, when I finally do that. Let me also write down this was -4 times C3 plus C1. -4 times the third column plus the first column.

Now before I actually do this, evaluate this determinant, let’s factor out as many constants as we can. For example there’s a common factor of 3 in this row, and there’s a common factor of 2 in this row. Actually I can factor the two out of the top row. Let’s factor all those things out.

So pulling a 2 out of the top row, leaves 0 0 1. Pulling a 3 out of the middle row leaves -3 1 1. Pulling a 2 out of the last row give me -13 -2 3. That’s a nice simple determinant. I’ve got 12 times, I’ll put some parenthesis here. So I’m going to expand along the top row. It’s going to be plus 0 times this minor, doesn’t matter it’s zero. So plus 0 minus 0 times this minor. Doesn’t matter if zero. Plus 1 times its minor which is this determinant here. -3 1, -13 -2. I still have the 12 out in front.

This is going to be 6 minus -13, so 6 plus 13, is 19. It’s 12 times 19. 12 times 20 would be 240, so 12 times 19 is just 12 less, 228. That’s our answer.