CHAPTER 04.09: UNARY MATRIX OPERATIONS: Theorems on determinants Part 1 of 4



In this segment we will talk about theorems of determinants. So letís look at theorem number one. Theorem number one says is a row or column of a matrix A, which is a square matrix of course, is 0, then the determinant of A is equal to zero. So what that means is that if somebody gives you a matrix and one of the rows or one of the columns you see is zero, then the determinant of the matrix is 0. So letís take an example. Somebody gives you like a 0, 0, 0, 6, 7, 9, -3, 2, 4, and someone says: what is the determinant of this matrix? You automatically can say itís zero without having to do any calculations because one of the rows is exactly equal to 0. Or somebody said: hey, can you find the determinant of this matrix here 0, 0, 0, 19, 3, 6, 7, -5, 20 letís suppose. In this case, one of the columns is exactly equal to 0. All the elements in that column are 0. The determinant of this matrix would be 0 as well. And that is the end of this segment.