Question Video: Determining an Element of a Matrix Mathematics • First Year of Secondary School

Video Transcript

Given the matrix 𝐴, which is equal to eight, negative three, 11, four, five, negative five, nine, two, negative one, 34, zero, negative seven, what is 𝑎 subscript two three?

This notation, a lower case 𝑎 and then two subscript numbers, is used to denote the position of one of the elements in the matrix upper case 𝐴. In general, if we were asked for the element 𝑎 subscript 𝑚𝑛, then this would mean the element of matrix 𝐴 which is in row 𝑚 and column 𝑛. So, 𝑎 and then subscript two three means the element of the matrix upper case 𝐴, which is in the second row, row two, and the third column.

Let’s find this element then in our matrix 𝐴. It’s in the second row and it’s in the third column. We see that the element in this position is the number nine. So, we can say that the element 𝑎 subscript two three of the matrix uppercase 𝐴 is nine. Remember, when we’re talking about the position of an element in the matrix, or indeed, the order of that matrix, it’s rows first and columns second.