Question Video: Finding the Number of Elements in a Matrix given Its Order Mathematics • First Year of Secondary School

Video Transcript

How many elements are there in a matrix of order nine by seven?

Remember, we arrange scalars, which we call elements, in a matrix in rows and columns. When we describe a matrix, let’s call this general matrix 𝐴, as an 𝑚-by-𝑛 matrix, it has 𝑚 rows and 𝑛 columns. And this matrix would look a little something like this. The order of this matrix is 𝑚 by 𝑛. Now we’re given a matrix of order nine by seven. And so this must mean that our matrix has nine rows and seven columns. So how many elements must it have?

Well, if we have nine rows and each of those rows has seven columns and there’s an element in each of these, then we can find the number of elements by multiplying nine by seven. Nine times seven is equal to 63. And so, in a matrix of order nine by seven, there must be a total of 63 elements. And of course, it follows that we can generalize this and say that a matrix 𝑚-by-𝑛 order must have 𝑚 times 𝑛 elements.