Question Video: Identifying the Determinant of a Matrix Minor Mathematics • First Year of Secondary School

Video Transcript

Consider the matrix 𝐴 equals negative six, five, negative three, two, six, negative eight, nine, nine, negative seven. Write the determinant whose value is equal to the minor of the element 𝑎 sub two three.

Let’s begin by identifying the element defined as 𝑎 sub two three. Suppose we have a matrix 𝐴 given by 𝑎 sub 𝑖𝑗. This means 𝑎 sub 𝑖𝑗 is the element that lies in the 𝑖th row and 𝑗th column. So the element 𝑎 sub two three is the element that lies in the second row and the third column. That’s the element negative eight.

Now, in fact, we want the minor of this element. The minor of some matrix 𝐴 is the determinant of some smaller matrix. And we find the smaller matrix by removing one or more of its rows and columns. In this case, to find the determinant whose value is equal to the minor of the element 𝑎 sub two three, we’re going to eliminate the rows and columns in which this element lie. So we eliminate the second row and the third column. This leaves us with a two-by-two matrix whose elements are negative six, five, nine, nine.

And so the determinant whose value is equal to the minor of the element 𝑎 sub two three is the determinant of the two-by-two matrix negative six, five, nine, nine.