How do the number of rows and columns of a matrix correspond to the number of its elements?
9
Practice makes perfect
We want to determine how many elements there are in a 3* 3 matrix. Recall that a matrix is a rectangular arrangement of numbers that can be used to organize data. To find the number of its elements, we must figure out what the notation 3* 3 actually means.
This means that the matrix in question has 3 rows and 3 columns. Let's take a look at the general form of this kind of matrix with a_(ij) being the number in row i and column j.
a_(11) & a_(12) & a_(13)
a_(21) & a_(22) & a_(23)
a_(31) & a_(32) & a_(33)
There are exactly 9 elements in all 3* 3 matrices.
Finding the Number of Elements for Any Matrix
To find a general rule for all matrices, let's look closely at the connection between the numbers in the given dimensions.
ccccc
Rows & & Columns & & Elements
3&*& 3 &=& 9
We can notice that the number of elements is equal to the number of rows times the number of columns. This fact holds true for not only 3* 3 matrices but for all matrices. To visualize this, we will consider counting the number of elements in a matrix as calculating the area of a rectangle with the same dimensions.
We can calculate the number of elements in a matrix simply by multiplying the number of rows by the number of columns. Finally, let's calculate the number of elements for other examples of matrices.
