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 are evaluating the determinant of this three by three matrix. And first up I'm going to write it a little bit bigger. So our first column is three negative 61. 2nd column is 245 and the 3rd 00 negative two. And when we've got anything larger than a two by two matrix, we can copy over the columns of everything except the last column. So I'll copy over the first column three, negative 61. And again the second column, 245. And now it's easy for us to multiply diagonally. So we take three times four times negative 23 times four is 12 times negative two is negative and the next diagonal is two times zero times one. Well that's zero and we'll add the third diagonal here, zero times negative six times five. Well that is also zero. So negative 24 plus two zeros is negative 24. And we're going to take that and subtract when what we get when we add together all of the diagnose going in the other direction. Starting in the bottom left corner and working our way upward diagonally, one times four times zero is zero plus five times zero times three is again zero plus negative two times negative six times two. Well that's 12 times two which is 24 zero plus zero plus 24 is 24. So we have negative 24 minus 24. Well that equals negative 48. We look at our answer choices and that matches with answer choice B. Well done, we'll catch you on the next one.