Question Video: Finding the Order of a Matrix Transpose | Nagwa Question Video: Finding the Order of a Matrix Transpose | Nagwa

# Question Video: Finding the Order of a Matrix Transpose Mathematics • First Year of Secondary School

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If π is a matrix of order 4 Γ 1, then what is the order of the matrix π^π?

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### Video Transcript

If π is a matrix of order four by one, then what is the order of the matrix the transpose of π?

In this question, we are told that a matrix π has order four by one. And we want to use this information to determine the order of the transpose of matrix π. To do this, letβs start by recalling what we mean by the order of a matrix. The first number tells us the number of rows the matrix has, and the second number is the number of columns. This means that matrix π has four rows and one column. We can use this to write down that matrix π is a four-by-one matrix with unknown entries π, π, π, and π.

We also need to recall that we can find the transpose of a matrix π by rewriting each row of matrix π as the corresponding column in the transpose matrix. In other words, we switch the rows and columns. We can use our representation of matrix π to find a representation of the transpose of π. We will do this by writing each row of π as the column in this new matrix called the transpose of π. The first row of π only contains a single entry π. We write this as the first column of the transpose of π. We can follow the same process for the second row of π; its only entry is π, so we write this as the second column of the transpose of π.

We can follow this same process for the remaining rows of π. We find that the third column of the transpose of π contains only π and the fourth column contains only π. This gives us the following representation of the transpose of π. We can see that it has one row and four columns. Therefore, the transpose of π is a one-by-four matrix.

It is worth noting that we do not need to directly represent the transpose of a matrix to answer questions of this form. Instead, we can note that taking a transpose switches the number of rows of a matrix with its number of columns. So, a matrix of order π by π, when transposed, will become a matrix of order π by π. We can then use this result to directly answer the question. π is a four-by-one matrix, so when we take its transpose, we will switch the order around to obtain a one-by-four matrix.

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