In Exercises 46–51, evaluate each determinant.

Question

In Exercises 46–51, evaluate each determinant. <Image>

Accepted Answer

Welcome back. I'm so glad you're here. We have got this four by four matrix and we're evaluating the determinant. First step is I'm going to write a little bit bigger. 5000 is the first column. Second is 5500. 3rd column is 5550. Cool pattern here. And fourth column is 55555555. And when we've got anything larger than a two by two matrix, we can copy all the columns except the last one over to make it easier to multiply diagonally. So I'll show you copying the first column, 5000 and the 2nd 5500. And the 3rd 5550. And now we can multiply diagonally, starting in the upper left and working our way down five times five times five times five. That's 625 plus the next +15 times five times five times zero. Well that is zero. The next 15 times five times zero times zero. Okay again, zero. And this last 15 times zero times zero times zero is a resounding zero. So 625 plus three, two zeros is 625. Now we're going to take that bottom total and subtract the total from multiplying in the other diagonal direction. We'll add all these together. So starting in the bottom left. Zero times zero times five times five. Okay, that's zero. Next 1, 0 times five times 5 times five is still zero. Next 10 times five times zero times five also zero. And okay. this starts with a five but times zero times five times five that is zero, adding all these is zero. We're taking 625 0 Which will give us 625. That is answer choice. D. Well done. We'll catch you on the next one.