More Determinants
Determinant is a type of function that can be used to determine the value of an element in a given matrix. The determinant is a single number that can be used to determine whether a matrix is invertible or not. Now, we need to define some terminology, so let’s say that A is equal to–well, what is it? Well, the definition of this will be that this quantity is equal to 1 times the determinant of what you get by looking in this lower right corner. And the 2 by 2 determinant- b2, b3, c2, c3. Then you subtract a2 times the determinant of b1, b3, c1, c3. Then you will multiply the determinant by and take a3 times b1, b2, c1. and c2. Each of these terms means that you multiply b2 by c3 and subtract c2 times b3 from this product, then subtract this product from that one, and so on. So there are actually six terms in the 3 x 3 determinant formula. Some of you may have seen a different formula for 3 x 3 determinants that lists six terms. It is the same definition; they are one and the same. Determinant in space: 3 vectors det(A, B, C)=|[a1,a2,a3][b1,b2,b3][c1,c2,c3]=a_1|[b_2,b_3][c_2,c_3]|-a_2|[b_1,b_3][c_1,c_3]|+a_3|[b_1,b_2][c_1,c_2]|
