CHAPTER 04.09: UNARY MATRIX
OPERATIONS: Theorems on determinants Part 1 of 4 In
this segment we will talk about theorems of determinants. So let’s 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 let’s 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 it’s 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 let’s 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. |