In Exercises 46–51, evaluate each determinant.

Question

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

Accepted Answer

Hello today we're going to be evaluating the determinant of a two x 2 matrices. Let's go ahead and recall what the determinant of a two x 2 matrices is. Suppose we have a two by two matrix C in the form of A B C and D. In order to solve the determinant, you're just gonna take the product of A. And D and subtract the product of CMB from it and that's going to give us our determinant. So in order to apply this to this problem, we're gonna take the product of four and 6 and minus the product of negative two and seven from that. So what that's gonna look like is four times 6 -2 times seven. Four times six is 24. And we're gonna subtract negative two times seven, which is negative 14 minus negative 14 is going to produce a positive value. So what we end up with is 24 plus And that's going to give us a total of 38 which is the determinant of this two x two matrices. That also means that the answer to this problem is going to be be So I hope this video helps you in understanding how to solve the determinant of a two by two matrix C. And I'll go ahead and see you all in the next video