Question Video: Finding the Number of Elements in a Matrix Given its Order | Nagwa Question Video: Finding the Number of Elements in a Matrix Given its Order | Nagwa

# Question Video: Finding the Number of Elements in a Matrix Given its Order Mathematics • First Year of Secondary School

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If the order of a zero matrix 𝑂 is 2 × 2, then the number of elements of the matrix = ＿. [A] 9 [B] 0 [C] 4 [D] 𝜙

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### Video Transcript

If the order of a zero matrix 𝑂 is two by two, then the number of elements of the matrix equals what. Nine, zero, four, or the empty set 𝜙.

Let’s begin by recalling what we mean by the order of a matrix. The order of a matrix tells us how many rows and how many columns that matrix has. In general, we can specify the order of a matrix as being 𝑚 by 𝑛. And this means that the matrix has 𝑚 rows and 𝑛 columns. We always specify the number of rows first and then the number of columns. The matrix we’re interested in in this question has order two by two, which means that it has two rows and two columns. It will therefore look a little something like this: two rows and two columns.

Now we’re actually asked to work out the number of elements in this matrix, so we can easily count them. There are one, two, three, four elements in a two-by-two matrix. That’s this option here. Now you may also realize that four is equal to two times two, the number of rows multiplied by the number of columns. And this is true in general. The number of elements in the matrix is equal to the number of rows multiplied by the number of columns. Now, in fact, the matrix in this question is a zero matrix, which means that every element is equal to zero. So the specific matrix we’re looking at is the two-by-two matrix zero, zero, zero, zero. But this doesn’t affect our answer. The number of elements in any matrix of order two by two is four.

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